Dude, you have *a lot* of stuff in your background. I am my departments background investigator. Honestly, i would send you a nice "Thanks but no thanks" letter.
Credit I don't care about.
Drug use....Ehh...There is a lot there. That would probably get you disqualified alone.
Work history: Not a huge deal, most people have been fired at one point or another.
Battery Charge: Sealed or not, it's still there. I will find it. Possible DQ
Hit and run: Felony, Probable DQ
Shoplifting with girlfriend: Probable DQ. You do have to tell me about it. Because I will do a detailed interview with you. We will go over your complete criminal history. Any lies or leaving things out will get you DQed. I will call your family, references, employers, friends I can find, friends that your friends give me. Ect. And if I get a hold of your girlfriend and she tells me about that and I can verify it with more people. You are done for lieing to me.
So all and all. There is some fairly major stuff here. One or two mistakes can be forgiven. However, you have a very nice track record of being on the wrong side of the law. My department is not going to take a risk on you.
I don't work for LAPD, maybe they will see it differently. But I doubt.
Consider the military, maybe 4 years of spotless service to your country will make you a better canidate. I know if I get an applicant will some issues in the past, the honorable military service can make me look past a lot of it.