alexsel - 9:45 pm on Nov 18, 2011 (gmt 0)

So, can / should I bid on their company name? It doesn't seem like anyone else is bidding on it.

You can. AdWords policy is to make sure you don't use other advertisers trademarked terms. That's not to say that your competitor might not contact you directly and have you remove the ads, but I very rarely hear of that happening. Should you? Why not. If anything it may help increase the CPC's of your competitors brand terms.

If I DO bid on their company name, how can I get a good quality score without getting myself into copyright / trademark trouble?

Use keywords that are as close to their trademarked term without infringing on their trademark. Either way, you are probably not going to see a high QS on these terms because you're not relevant. If you get anything higher than 5-6, I want to hear about your magic bullet .. ;)