After seeing the video several times, I'm still unclear as to one or two details of the murder itself.
The murderer went to the scene of the crime on horseback, right? After discovering the victim, Harriet noticed his footprints on the sand, but no others except her own. A few days later, she also found in the sand a horseshoe that had fallen off the horse. So why didn't she ever see the horses's footprints?
I think it was because the murderer approached and departed from the opposite side of the rock that she was on and she didn't look over that way. At one point, Lord Peter hid behind on the other side and asked her if she could see him. That's when she realized the murderer could've been there when she found the body. I also think (although I'd have to watch again to make sure) that they said something about the horse's footprints being washed away. They found the horseshoe near the water's edge and the water would've washed them away there. I'm not sure but I think they thought the murderer rode the horse up to the rock and climbed up which wouldn't leave the killer's footprints.
**spoiler warning** Well, this is quite a while later, but if you are still wondering...the horse's hoofprints were washed away by the tide. Paul Alexis had been dead for a few hours by the time Harriet came upon him, and the tide had gone out and was coming back in. That was why the timing of when everything happened was so important. If it had happened, as it had at first seemed, just before Harriet found him, then there should have been prints of some kind in the sand.
The blood was still wet because Paul Alexis was a hemophilliac--his blood wouldn't clot so Harriet could have found him a couple days later and the blood would still have been wet.