I don't know the details on the Blood Atonement, but the LDS Church does continue to hold some sins as "unpardonable" and that forgiveness cannot be received in this life.
- Sons of Perdition - Those who served Satan and turned utterly against God.
- Shedding of innocent blood (murder)
- Denying the Holy Ghost after receiving a sure knowledge
Denying the Holy Ghost after receiving a sure knowledge is not a very common sin to occur. Most of us will not receive a sure knowledge in this lifetime (based on my understanding).
Oftentimes suicide is grouped into shedding of innocent blood, but the reality is that taking of ones own life is much more complicated and may actually be considered murder by a 3rd party in the eyes of the Lord. The point being that we cannot judge those as God would.
Likewise abortion is the shedding of innocent blood. Again this is a complicated matter when the life of the mother is at issue, or cases of incest or rape.
There is a scriptural & doctrinal support for capital punishment for example in the case of murder, but the LDS Church does not have an official stance on it. The LDS Church does however officially oppose elective abortions (follow link for full details).