If no one else said it yet: DO NOT EVER EVER EVER MESS, JOKE, LAUGH, POINT, FROWN OR SMILE AT THE LAPD.
My experience is that they live up to every bit of their terrible reputation as a gang of mean (& racist) thugs.
They're the nicest cops I've met.
Congrats on your luck.
In my three years of living there (border of Hollywood and Silverlake), my experience was -
1. Seeing them kick (literally) an old homeless woman down the road. She was laying against a palm tree in the devil's strip to escape the sun, and wasn't drinking or anything.
2. Called my wife a liar to her face the second day we were there. They pulled her over for some reason.
When she showed them her NYS driver's license and explained that she just moved to LA, they called her liar and threatened to haul her in, blah, blah, blah. They ended up just writing her a ticket, but she was balling her eyes out the whole time. The officer laughed at her and told her to stop crying like she was faking the whole thing. She actually thought about moving back to NY after that. We'd been there two days.
3. Heard numerous stories of them targeting friends of color (black, latino, etc.) specifically for harassment, etc.
I quickly learned to avoid them at all costs. If I saw an officer on foot, I would literally cross the street to walk on the other side. Was I paranoid? Would I have been fine? Maybe. But I'd never seen anything like them anywhere else I've lived. I'm sure there's nice cops there, but by and large, they are a messed up organization.