First, the fundamentals:
Check oil level and condition.
Check belts for cracking
(3 series)Check for rust color on top of alternator
Look at the service indicator. Does it say (-3000 miles) or have the yellow and red LED's lit?
(X5) Check the Axle boots. If they're blown it can add up to big bucks!
Make sure the coolant looks good. Green coolant is a sign that someone who shouldn't be working on the coolant system did.
The best advice I can give is to ask the buyer if you can take it or have him take the vehicle in to see your trusted BMW mechanic. He has the eyes you need to get the best deal.
ALSO, If you can, NEVER BUY A CAR THE SAME DAY YOU'RE LOOKING!
I have stuck to this rule and never had a problem. A 10-40,000 dollar purchase is something you need to think about and never should be done on an impulse. Give yourself at least 24 hours and then go back if you're still interested. Trust me.
There are a bunch of other things you need to look at but all this stuff is flying off the top of my head (hey it's a forum, not my college english class) so please bear with me.
Any questions or if I can be of any help please let me know.
Joshua