The differences in this second edition are minor.
The original pre-order of Combat Commander did include 2 bonus scenarios (#101 and #102) that were not included with the second printing. These bonus scenarios are now available for download from GMT's site.
fixed German card #48 (called its order an action)
fixed pillbox count on American cheat card (information only, no impact on game play)
pinlines added to the hills on maps 11 & 12 for clarity
There were some cosmetic changes between the two printings. The maps are back-printed (meaning there is a map on the front and back of each mapsheet. The paired up maps are a little different:
First printing: 1/4 2/3 5/8 6/7 ....
Second printing 1/2 3/4 5/6 7/8 ....
Another cosmetic change...the counters on the first printing countersheet are only connected at the corners. The counters on the second edition of the second printing are also connected in the middle of each side. This results in a small tab that might be difficult to remove if you trim your counters.
See this comment for links to more info.