How can I research a domain that I may want to purchase?

Google’s Matt Cutts was asked a question at Google Webmasters about buying a domain name:
Question: How can we check to see if a domain (bought from a registrar) was previously in trouble with Google? I recently bought, and unbeknownst to me the domain isn’t being indexed and I’ve had to do a reconsideration request. How could I have prevented?
Wally, Reno

This is his video reply: