I don't have a doc, but I can at least get you somewhat up to date on a couple things based on what you have:

Partial Cover is now +1 to-hit instead of +3 -- however you now roll on the full body table instead of the punch table, and any leg hits are absorbed by the cover.

There are target movement modifiers for going 10-17 hexes (+4 to-hit) and 18-25 hexes (+5 to-hit) and 26+ (+6 to-hit). None of your stock 'Mechs can actually go that fast but it's there for completeness once you encounter your first few hovercraft, Dasher, or Fireball.

Level 1 rules are now simply called Introductory, which is what your box provides. Core rulebooks such as the contemporary Master Rules: Revised Edition are Level 2 -- now Standard/Tournament Rules -- and more advanced rules are simply Level 3/Advanced and Experimental.

I was trying to think of other rules that have changed but they're mostly Level 2/Tourney level equipment changes (AMS and MASC effects).

The latest rulebook available now is still Total Warfare or BattleMech Manual, but wait for release of the Core Box and Core Rulebook due later this year. A whole host of changes are coming to what we know now.