When an entity rides a minecart, sometimes, launching the minecart (using powered rails for instance, or pushing the minecart) leaves the entity (eg, Villager, Ghast) where it was. Yet the entity is actually moving with the minecart because upon relogging the entity is again shown in the minecart (and left at the place where it was when you relogged, while the minecarts keeps going)

So while the entity is shown immobile, it is actually moving (typical example: I use ghasts the flush mobs, the ghasts aren't moving while the mobs are "magically" pushed by the invisible ghasts riding the minecarts). However, the immobile entity still keeps its collision box, meaning that if you go to the spot where it is displayed (hence not its actual spot cause it is inside the minecart), you get pushed away by the "fictious" entity.

This behavior seems to also happens once you go past the render distance of minecarts. (Ie, place the entity in the minecart, go past the render distance, or unload the chunk, come back and start the minecart) - so it seems the issue is client side.

This has sometimes the following consequences : if you have a loop with two minecarts, both holding a Ghast, while you expect the minecarts to loop around indefinitelly they actually spot : one minecart collides with the "fictious" immobile Ghast and stops, cause the second minecart to collide with the stopped minecart and to stop too. (This breaks some awesomely fast farms) (Though this seems to be a different bug happening server side - I have not yet witnessed it in singleplayer - but I must say I haven tried.).

Screenshots 1-2-3 > Both Ghasts are correctly moving in the minecarts.
Screenshots 4-5 > One is moving, the other is out, but immobile (displacement was caused by me pushing it)
Screenshot 6-7-8 > both minecarts seem empty - yet ghasts are inside, and they don't move on their own. (and note on screenshot 8, ghasts are partially inside the blocks - with the new collision mechanics, they'd be pushed away if they could move - they are not!)

Note on the sceenshot: one of the ghast is standing "outside" the minecart but is not moving: he's actually inside the minecart, hence can't move on its own (it was summoned using a spawn egg, so it has a AI). You can push the ghast "outside" the minecart and it pushed you back, but you cannot hit it. Then on the next screenshot (taken after) both ghasts seem to be out of the minecart, while they are actually both in.

Note that going pas the render distance then coming back again updates the positions of the entities, but they still remain immobile.