What changes to the rules if any, have occured between second and third edition. Are they similar enough to, say, take an adventure from SR2 and adapt it for SR3?

Very easy to take a SR2 published adventure and run it in SR3. The types of changes I recall are (a) replacing Firearms and Armed Combat with appropriate 3rd Edition Skills [you can do this on the fly], and (b) using Combat Pool instead of Threat Pool [on the fly], and ( c ) picking appropriate 3rd edition spell [on the fly].

Though with many people in the opposition I find it easier to still use Threat Pool.

Another change is the was initiative works. Used to be that people with extra actions got theirs in the begining of the turn, now they get it at the end.