This thread should become a sticky - there are a lot of good tricks and tips that have been mentioned so far. My 2 cents worth is:
1- Universally, the worst LPs as a class are rock & roll; especially "classic rock". It's so bad that I won't even bother to inspect a used Beatles or Stones LP unless I know or trust the seller.
2- Conversely, the best class is almost always classical and opera. As someone mentioned, box sets are almost always a good bet. Pay attention to your label and who actually made the LPs, though.
3- I won't buy any LP that smells of mold or mildew. This tens to be a big prolem with garage sale LPs, in my experience. I know that I can clean them up, but I'm not going to take the time and I just do not want them in the house.
4- I won't buy scratched albums, period. It's just not worth it. Inspect all sides of all LPs in a multi-album or box set, but 99% of the time Side 1 is in the worst condition.
5- Learn to recognize the differences between scratches and scuffs on the LP surface that are not audible.
6- While I prefer pristine album covers (who doesn't?), most aren't. Some labels used poor construction and/or bad glue, especially some import labels. If the LP is in good shape it's still worth buying, assuming that it is not water damaged. See note 3.
7- I agree with everyone who has stated that vacuum cleaning is a must. I do not like the Spin Clean for deep cleaning, it just doesn't get the job done for me. But I do think that it's handy as a pre-cleaning device to get the surface dirt off of the LPs before I take them to the VPI cleaner.