This answer will examine the theological implications of theistic evolution within a Reformed theological framework. This will not include matters of hermeneutics, that is, interpretation and epistemology of the text of the Creation account itself. Where Reformed theology derives doctrine from the text may be referenced, but I will not be contending with the meaning itself, but accepting its established meaning from this perspective.
Federal Headship: Christianity, by definition, believes in Christ. It believes that Christ saved Christians from a problem we all have in common through his work. In order to save people, Christ had to apply his saving work to many people. For such a work to apply to many people we must have a mechanism, or paradigm. In Reformed theology, this mechanism is understood as Federal Headship. Adam was mankind’s representative and head.
Original Sin: The problem that all people have in common is sin. While each person commits their own sins, they each are guilty of sin and affected by sin’s corruption regardless of their own actions. Adam’s sin introduced sin to mankind and, as the first man and Federal Head, imputed his guilt to all of his descendants. This inherited guilt and sinfulness in all mankind is Original Sin.
Romans 5:17 (ESV) “For if, because of one man’s trespass, death reigned through that one man...”, 5:18: “Therefore, as one trespass led to condemnation for all men...” 5:19 “For as by the one man’s disobedience the many were made sinners”
The Fall: The historical moment that original sin occurred and its consequences entered creation. Death may or may not have existed before the Fall, but regardless, sin entered creation, or at least man, at the Fall.
General Revelation: The doctrine that basic knowledge of God’s character and attributes may be observed in nature. Just as any piece of art or writing or work of creativity will reflect aspects of its creator, we gain knowledge of God’s existence, power and attributes by examining His creation.
(Psalm 19:1-2, Romans 1:19-20)
Materialism/Physicalism: Anthropological Materialism/Physicalism is the belief that only mankind is only made of natural, physical material. All life, consciousness and thought are results of physical substance and activity.
Dualism: Philosophically speaking, the concept that the physical flesh is evil and the spirit is good. Rejected by Reformed Theology. 
Headship of Husband: That mankind was made male and female, but that in the union of husband and wife, the husband is the head over his wife. This is compared to how Christ is head of the church and the Father is the head of Christ.
I. No Historical Adam & Eve
A. No Federal Headship
B. No Original Sin
C. No Mechanism for Christ’s Work
II. Historical Adam & Eve
A. Eve was not “from Adam”
B. Interaction with Old Man
III. Nature of Man
A. Image of God
B. Constitution of Man
IV. Character of God
A. General Revelation Obscured
B. Trial and Error: It is Good?
V. Nature of Sin
A. Sin not Origin of Death
B. Sin not Imperfection/Corruption
I: No Historical Adam & Eve
As it has been noted, (thank you, Marc Gravell), from an evolutionary viewpoint, there can be no “first man” or one, historical, Adam. There is no sudden, perceivable change where within one generation one can point and say to one “yes, that is a man” and to the other “no, that is an animal”. Not unless we define the change in Adam purely as spiritual and God’s breath as the moment that made him change from animal to man (see Section II).
Federal Headship: If there is no Adam, there is no first man to represent his race. 
There is also no original sin. This means sin did not enter the world through one man, but instead through the failures of a whole race for generations. And if there is no Adam, and there is no federal headship, then there is no universally inherited sin and guilt by imputation to all who are “of Adam”. Original sin becomes inherited error or imperfection, but not inherited guilt.
Mechanism for Christ’s Headship:
If there is no Federal Headship then there is no mechanism for Christ’s righteousness, just like Adam’s sin, to be imputed to all believers. Adam is said to be a type of Christ to come (Romans 5:14). With no Adam, there is no type for a future Christ.
Federal Headship “was the only way it would later be possible for God to save us once we had sinned.” 
II: Historical Adam & Eve
In order to avoid (some of) the issues above, one could claim that theistic evolution advanced the biology of man’s bodies forward enough to where God stepped in and made him a living soul. It could be this moment that we see the historic creation of one man, Adam, from a spiritless humanoid animal to a spiritual being with the image of God. Now we have evolution and a historical creation of one Adam.
Eve not “of Adam”:
The only problem with this is that in this model creation the physical aspect of man is already existent. And, necessarily, Eve also is existent, she came from physical parents some time before this moment. But this would mean that Eve is not made from Adam, not physically “bone of my bone, flesh of my flesh”. (Unless, of course, Adam was Eve’s father, which I’m still not sure would solve the problem and is a bit alarming in and of itself.) Eve would have to also receive the same special creative interjection by God to make her a living soul as well, otherwise she is just a human “beast.” Either way, if Eve is not “of Adam” physically and spiritually then it is difficult to assert male headship in the union of a husband and wife. 
Interaction with “Old” Man:
Having a historical Adam picked out of an existing species brings up the awkward situation of having two “races” of men that are of the same species and are genetically indistinct. We have the new “living soul” man, and the old beastly man without a spiritual aspect from God. This only becomes interesting when we consider how the spiritual nature of man would impact such interactions.
III: Nature of Man
This then leads us to questions of the nature of this new human race.
Image of God:
As mentioned above, man’s physical nature is either all he is through evolution (materialism) and no historic Adam, or it precedes the giving of a spiritual part to a Adam. The image of God in man cannot be reflective of man’s whole being, it can only refer to his spiritual part or his physical side alone. Not both. Or, the image of God in man simply does not exist.
One might say that the physical man’s evolution was directed by God and therefore reflected God’s image and then was later combined with the spiritual image. However, this is difficult to see as will be discussed further later.
With no historical Adam, there is no moment of creation where God would impart an immaterial, spiritual part to Man. Theistic Evolution demands a monist understanding of the constitution of man. Mankind is purely physical. The only other alternative is that all life (from evolutionary precursors) has an immaterial aspect, even now, including plants, fish, dogs, etc. This immaterial aspect would have to be equal in all stages, or somehow be gradient in its relation to the sophistication of the creature (culminating in man).
However, if there were a historical Adam and we view the material evolution as a necessary evil and God's moment of creation being just to provide a spiritual aspect to Adam, we may be inclined to fall into a form of dualism. As we will discuss in the next section (IV.B), it may be difficult to look at the physical evolutionary process and say "it is good". Much like the Image of God, because there is not one moment where the entire man, physical and spiritual, is made, we could fall into the trap of assigning more importance to one over the other.
IV: Character of God
General Revelation Obscured:
From a Reformed perspective, we can imagine God creating all that a man is in a moment and wonder at the wisdom, the creativity, the foresight, and the beauty of the design. We can reflect on what this God must be like who can imagine our cells, our brain, our nervous system, our senses, and our consciousness and the power it displays to form it in an instant.
On the other hand, from a theistic evolution extreme, it is difficult to discern what was the product of this God’s wisdom, creativity and intelligence, and what was the product of random natural selection.
These are clearly two polar opposites and there may be middle ground, but theistic evolution, by nature of how it functions, obscures the clarity of God’s General Revelation. Suddenly it is not quite so easy to know who God is, or (as fully naturalistic evolutionists propose) to know whether there is a God at all. The knowledge of God to all mankind is a core doctrine of Reformed theology.
No longer is man “without excuse” if he claims theistic evolution, for it is not nearly as “clearly perceived” as it used to seem. (Romans 1:20)
Trial and Error:
Natural selection requires trial and error by definition. For God to use evolution would require the death of countless generations of failed specimens. Can each “day’s” creation really be declared “good” when there is so much failure in each age. This leads us to the General Revelation that God is either not Sovereign or not Perfect. The only alternative is to claim no mistakes were ever made and the right mutations always happened, every generation, every species, to lead to Man. This is so contrary to evolution that it cannot even be called such anymore. There is no difference, in fact it becomes pointless to distinguish, from simple creation ex nihlo.
V. Nature of Sin
Origin of Death:
As we saw in an earlier section (I.B), there can be no Original Sin with no Adam. Even if there is Adam and Original Sin, sin cannot be the origin of death. Death is a neutral, and necessary, phenomenon which may occur as a result from sin, but is not originally caused by sin. The only scenario this would be possible is if man evolved to the point where he would not die, but by sinning God cursed them to death.
Sin is not Imperfection or Corruption:
The nature of evolution requires mistakes and mutations. However, since these occurred before Adam (or without him) as God’s chosen process, sin cannot explain the entropic results. Even now, when a child dies due to a genetic mutation we cannot see this as the effect of sin on creation, but rather as a necessary. It is not just a divinely condoned event, it divinely directed and mandated.
The following is a review of the Reformed theological doctrines that are impacted. They must either be redefined, re-evaluated or replaced for one to remain theologically consistent.
The theological implications of theistic evolution are:
With No Adam:
- No Federal Headship of Adam over the human race
- No Inherited Sin or Guilt from Adam
- No Federal Headship for Christ's Imputation to believers (a different mechanism for salvation is needed)
- Demands Materialism, no spiritual aspect to man.
Even with an Adam:
- The Image of God in man is either only physical or spiritual, not both, or nonexistent.
- Suggests Dualistic dichotomy that flesh is evil and spirit is good.
In all theistic evolution models:
- No basis (in creation) for Headship of the Husband in unions.
- Death is not a result of Sin and The Fall
- Sin is not imperfection or corruption (which in a materialistic model is a bit of a paradox, since it can’t be spiritual)
- Clarity of God’s character through General Revelation is obscured in nature.