Let's see, off the top of my head (I'll consult the copy I got at Origins when I get home from work):
- Terrain modifiers (woods and partial cover both went from +2 to +1)
- TMM loss from heat and damage (no longer have to memorize or look up the table in the book; it's not there anymore. Half MP is also half TMM, and the second point of heat drops the TMM by 1).
- JMPW# and JMPS# replace looking up the 'real' TMM for jumping movement; you add +1 to your normal TMM for jumping like usual, then modify that number based on the #. A Jenner D's (14"/10"j) TMM is +3, jumping is +1, JMPW1 is -1, the Jenner's jumping TMM is +3. Slightly more steps if you already had everything memorized, significantly easier if you didn't.
- Lance/Star formation building got tweaked a bit, too many small things to list here.
- Building a full Company (or bigger) force with Special Command Abilities and that cool stuff is reworked slightly to be more intuitive.
I think those are the big ones that affect primarily 'Mech/vehicles.
EDIT: it's also improved significantly in layout and appearance. If you have the BattleMech Manual, it resembles that aesthetically. Which is a major improvement in my estimation.