Those at USC, is the attitude that current employment prospects are better or worse than last year?
Although the 2Ls on here are better qualified to answer this, the general feeling is that things have been continuing to improve since the 2008 recession. Current employment prospects are probably slightly better this year than last year.
Does the USC/UCLA rivalry put one at a disadvantage if they are being interviewed by an associate from the "rival" school?
Regarding any potential disadvantage, I seriously doubt it. Employers who are graduates of either school know that USC and UCLA are both very good law schools and you likely won't be at any disadvantage whatsoever when being interviewed by a graduate of the other school.
I echo what chimp said. And for the second question, it's great to run into a USC alum during an interview but no one's going to ding you for being from either school. Also there's a decent amount of crossover (USC undergrad/UCLA law and vice versa).