There exists a new (?) glitch which can save time at many places throughout the game. I first saw the technique in a video by Fusionbly, after which I did some testing and found more uses to it.
Basically, object and ledge activations that (can) make Abe 'auto-turn' can be delayed and done somewhere else instead by cancelling to running while auto-turning is taking place. The most useful application to it is delaying climbing down ledges~~
(link removed. see the one below instead)
Ledges above Abe work similarly, but the use is more limited since Abe won't actually grab a non-existant ledge above. He just jumps 'up' like he always does when prompted, or so it seemed when I tested. There is at least one use to it, though, and it is being able to get a standing Abe inside crawlspaces: you can do the upwards jump from rolling stance, and afterwards Abe gets up standing like normal, being able to jump over mines blocking the crawlspace, chant, etc.
http://www.youtube.com/watch?v=fIzm6iWHRtU
Elevators are subject to the glitch too, but nothing good comes out of them. On normal ground game crashes, and on objects... well, see for yourself (a demonstration from Fusionbly) (EDIT: link updated).
http://www.youtube.com/watch?v=Nun5mMi5q80
Finally, and again useful, is Elum teleporting. It's the same mechanism. The simplest known use is getting on glitch-Elum while the actual Elum is in the same screen: Abe instantly travels back on him.
http://www.youtube.com/watch?v=iUUjdruvB_4
If Elum is in a different screen, Abe still teleports on him but the camera won't follow. It's possible to glitch-move the locations of elevators by a few steps while doing this, for some reason. Trying to move to new screens while out of camera yields strange results, at its worst making Abe and Elum fall off the screen. However, if there's a screen below (e.g. somewhere you can fall to safely), this phenomena can probably be utilized for skipping things as well. (EDIT: link updated)
http://www.youtube.com/watch?v=LL238yaoosU
There are other small oddities concerning these things too, but probably of no consequense. (including getting a "small Abe" in normal gameplay, making Elum disappear, getting on an glitch-Elum which won't move, etc.)
http://www.youtube.com/watch?v=56-586wJkfs