Until Mary Schweitzer's discoveries of soft tissue it was scientific orthodoxy that soft tissue could not remain as soft tissues for more than a few thousand years: the oldest soft tissue until her finds were in Egyptian mummies. Once she found supposedly much older soft tissue, amongst the scientific community that stopped doubting her, there was a huge amount of scrambling around looking for scientific explanations for very old soft tissue in order to ensure that uniformitarian notions of the age of the earth and the dating of the era of the dinosaurs remained comfortably, though it must be said a little more precariously than hithertofore, intact. On the face of it it is absurd to me for anyone to believe that any soft tissue at all can remain intact in a dinosaur fossil eighty million years old.
We are constantly bombarded with very accurate assertions of the dating of various fossils and periods in the uniformitarian model: a couple were wandering around a museum and came across a fossil which had no notice indicating how old it was, and they really wanted to know. They could only find a man sitting at the entrance to the museum room, (who was keeping an eye on the visitors), so they asked him he knew anyone they could ask. “Actually I happen to know myself: it is 78 million years old and two days.” “That’s incredible! How can you possibly, possibly know it so accurately?” “Ah, well, you know”, he said, “a scientist was taking a guided tour around the museum and I overheard him say that that fossil was 78 million years old and that tour was the day before yesterday.”
Dating, such as that of the K-Pg extinction event at exactly 66 million years ago mentioned in the OP's question (how is it known it wasn't 65 million years ago... or 67... or 60 or 70 million?) is laughably absurd, and probably only designed to pull the wool over the eyes of the unscientific masses. But, more, it must come as a bit of a shocker to discover it is impossible to arrive at any dates at all without making rather sweeping assumptions.
The only direct way you may be able to date a long-dead creature or fossil is to use radiocarbon dating and compare the quantity of the different isotopes.
A continual process occurs with cosmic rays bombarding the upper atmosphere producing fast moving neutrons; when these neutrons collide with nitrogen atoms they produce radioactive carbon 14. This gets used the same as "normal" carbon in plant tissue which gets eaten by animals. When the animal dies it has a ratio of c14 and c12 comparable to the ratio in the atmosphere. From the point of death the ratio of c14 to c12 begins to alter as the c14 decays. If we assume that the ratio of c14 to c12 has not changed in the atmosphere throughout the earth's history then it is possible to arrive at an age for long-dead organic material, both animal and vegetable. But radiocarbon dating can only possibly give meaningful measurements up to about 40,000 years old because the half-life length of decay is only 5700 years: every 5700 years there is half as much c14 at the end as there was at the beginning. So, because of the relative shortness of the half-life, even if the assumption that the ratio of c14 to c12 in the earth's atmosphere has remained constant is a correct assumption, it is not possible to date fossils supposedly millions of years old using this method.
Other isotopic dating methods
Uranium has a half-life of 4.5 billion years and decays by a series of steps down to lead. But uranium is not absorbed by animals and, apart from c14, no other radioactive isotopes are absorbed by animals either (so no other r-active methods can be used to date fossils directly). So the only way to date fossils is to try to date the rock layers in which a fossil is found. In the case of uranium and lead, three different ratios have been tried in the past 238U verses 206Pb, 235U verses 206Pb, and 207Pb verses 206Pb, These three methods have typically been tried on the same rock strata. If the three different methods come up with the same age for a rock then that gives some confidence for the age of the rock. Unfortunately this three pronged method almost never comes up with any useful date. And there are assumptions with this method: first it is assumed either there is no leakage or we know the extent of any leakage either into or out of the rock of both the uranium and the lead. In fact “uranium is often in a form that is readily soluble in weak acid” (Dr Sylvia Baker, “Bone of Contention”, 2002, page 23). Secondly, we must assume that the rate of decay has remained constant. And thirdly, and most important of all, we must make assumptions about the amount of the uranium and lead isotopes that the rock started with in the first place. (These three assumptions have to be made irrespective of what radioactive method you use, whether it is uranium/lead or potassium/argon or whatever.) And it is this third assumption which is the most decisive of all in dating a rock layer.
In point of fact because of this third assumption, and because radioactive dating methods almost invariably vary so wildly by hundreds of millions of years, it is currently impossible to date rock layers and thus it is impossible to date the fossils found in the rock strata. So, for instance, the K-Pg extinction dated at 66 million years ago: we do not currently have any scientific method which can tell us whether it was sixty six or sixty five or sixty seven or twenty five or twenty seven or five or seven million years ago or even less than one million years ago: scientific methods have come up with no reliable date.
In view of the failure to date rock strata by isotopic methods geologists have fallen back on another method: they have based the age of a strata on the supposed age of the fossils found in the strata. Oblivious of the palaeontologist’s reliance on geologists in dating the age of the rock by geological/isotopic dating methods, the geologists have perhaps inadvertently resorted to gigantic circular reasoning for dating the rocks: the palaeontologist looks to the geologist, and the geologist looks to the palaeontologist, and it must be such and such an age because everybody says it is.
As a Christian I am free to examine the evidence for and against evolutionary theory to a much greater extent than the agnostic and the atheist. For them it is really the only intellectual fig leaf behind which they can hide. But the Christian does have differing options and I fully expect there is a multiplicity of views held by Christians in this site. I used to believe in evolutionary theory and even loved it. After becoming a Christian I became a theistic evolutionist. Finally I am now a six day creationist. To me now, evolution is:-
a) impossible because the first living self-replicating creature could never have come into existence naturally. It is impossible because the simplest living thing we know of has DNA and RNA and several hundred different kinds of proteins. These proteins are produced by the DNA and RNA and yet the DNA and RNA need proteins in order to work – an impossible catch twenty two chicken and egg situation. And
b) Unnecessary. God tells us how he made the world, there is no reason to disbelieve him. (But I do not believe that Genesis 11 gives a father to son genealogy, and so am ambivalently ready to believe the world might be anything up to maybe 50,000 years old. Studies on Mitochondrial Eve and y-chromosomal Adam (it should really be called Noah) one day might usefully provide a clue for the date of creation and of the flood. And evidence from Egyptian archaeology fits beautifully with the Bible account of Joseph and means the flood must have happened long before 2500 bc.)
A few years ago some creationists sent several dinosaur fossil samples to a reputable radiocarbon dating institute to be dated. The institute did not know they were dinosaur fossils nor did they know that they were being sent by creationists. If I remember rightly the institute continually returned ages of the fossils of around 22,000 to 40,000 years. When the institute realized what was happening they refused to date any more samples. Long live free scientific enquiry: “The truth no matter where it leads!”
For further reading
On evolutionary theory
“Bone of Contention” by Sylvia Baker – short and sweet, and very clear
“Darwin on Trial” by Paul Johnson
“Signature of the Cell” by Stephen Meyer
“Evolution” by Colin Patterson (an evolutionist, but the book does not dodge the problems with evolution getting started)
Not just evolutionary theory
“Show me God” by Fred Heeren
“Just Six Numbers” by the Royal Astronomer, Martin Rees
And one of my favourite youtube videos!
“Atheist physicists prove God: Anthropic Principle fails” by Helasmoh Channel (13 minutes) https://www.youtube.com/watch?v=z4E_bT4ecgk&t=29s