This has happened TWICE with different minecarts at the end of an unfinished mine rail.

Problem:
Tried everything in attempt to get off minecart but CANNOT get off minecart at all.
The bug enables me to hit/destroy the block underneath minecart and surroundings, but character remains STUCK in the minecart unable to move.
Destroying block underneath through the minecart takes a long while.
Right click (to get off) won't work.
Left click (to destroy minecart) won't work. It just hits through.
The Mine rail is built off the ground, about 5 blocks high, so attempted to destroy the block underneath and fall but minecart still wouldn't detach from the character.

Along with many other new bugs encountered, this problem has never occurred until the latest update from Minecraft 1.5.2 to Minecraft 1.6.1.