The first issue is the one that I have most often. When a player comes close to landing on a jump through but not quite making it, their Y drops to 0 for just an instant and then they begin falling again. The causes some real issues on games where you are trying to design for tricky jumps.
I have found that it happens regardless of how thick the jump through is. Ashley any word on this? It makes pixel perfect platformers not so pixel perfect as the jump arc gets pretty messed up when a player comes close to a jump through platform.
This can also be seen when falling off of the edge of a jump through if you immediately hit back toward the direction of the platform. SO run off and then immediately reverse direction back toward the platform and you will see the same behavior.