I've found multiple problems with slimes when they are inside of minecarts. Here is what I have found:

1. Slimes in minecarts maintain their speed permanently on rails including normal rails, so one powered rail can power the minecart permanently with a slime inside. The minecarts do behave properly when off of rails, such as if the minecart slides off of tracks onto a grass block.
2. The slimes maintaining this speed continues even if a powered rail is attempting to send the slime in the opposite direction. It appears that the speed can increase, but cannot reverse direction or decrease.
3. I did manage to get the slimes in minecarts to change direction at one point, however it made no sense. In the middle of a line of normal rails, with no blocks around besides the blocks directly under the rails, the slimes continued to reverse direction at two specific rails.

To recreate this bug just create a line of powered rails and create a slime in a minecart on one end of the powered rails. When it reaches the other end of the powered rails, it will not reverse direction as it properly should.