LA is not among the bike-friendliest cities in the world. I won't tell you not to run over peds (that's obvious) and to always expect them to move unpredictably (that's obvious too), but a lot of people don't realize what a hazard every driveway and intersection presents if you're biking on the sidewalk. Drivers pulling out of driveways, or turning into/out of cross streets won't see you, so you should always slow down before driveways and intersections and make sure the way is clear before you proceed.

Will the police give you a hard time? I don't know since I'm not from LA, but I doubt it. If anything, they probably expect people to be riding there in the first place - a lot of cops are ignorant of the law as it applies to cycling.