I'm helping a friend of mine move back to L.A. from Canada, so I'm being her eyes, so to speak. Here are some useful tips:
1. Look at the way the outside of the building is kept, including the landscaping, condition of the pool, etc. If it doesn't look good, if there's trash all over the place, etc., there's a good chance that you'll have trouble with even routine maintenance issues.
2. If the owner/manager is too lazy/cheap to thoroughly clean the carpet and remove any stains, replace the scratched and worn linoleum in the kitchen, etc. then again, routine maintenance issues probably aren't high on their priority list.
3. If the apartment complex itself seems a bit "tired", if there are children running around screaming with no supervision, etc., then you might not want to live there even if the apartment you're looking at has hard wood floors, granite counter tops, etc.
4. If an apartment manager/owner is willing to show you an apartment that has dozens of dead roaches on the counter tops (yes, this really happened to me once!), you might not want to live there.
5. If the apartment has no central air, be sure the windows don't face east and west unless there are huge trees overhead providing shade.
6. After you've seen the apartment, come back another day and ask other renters if they like living there, and what they really think.
7. Don't pick an apartment on a busy street unless you like hearing traffic, people honking, etc. at all hours of the day and night.
8. Amenities like a pool and an elevator are less important than a quiet, well managed building.
9. If there are abandoned cars on the street or nearby, you might want to continue your search.
10. If it makes you shudder to think of the manager having keys to your apartment, that's probably not the place for you.
Please feel free to add to this list!