Do the Steam versions of the X-Com games have the original bugs fixed?

No, the game is exactly the same as the original, run through DosBox.

Still a great game to play though :)

The Steam version still uses the original game. None of the bugs are game-breaking, but they are worth knowing about.

Check them out Here.

My favorite? The Paying for Dirt bug. Be mindful or you will wonder where all your money went. :)

There is a software tool called Xcom Util (http://www.bladefirelight.com/) ( referenced on the Steam forums here along with Steam install instructions :- http://forums.steampowered.com/forums/showthread.php?t=1113400) that fixes some of the bugs and adds a number of helpful features and tweaks to improve the game. It's certainly worth examining.