Drunk driving has always been an issue in most of America. It's not taken seriously. In Houston there was regularly horrific DUI deaths and people wouldn't bat an eyelash (several times there were cars driven by drunks onto the freeway *on the wrong side. Bam, four killed. Doesn't make top story on the local news).
I'm sure it's a big issue but I don't think it's any worse than most other large American metros. In fact, I imagine it may be less of an issue here. LA does actually have a somewhat functional rail/bus system and some pockets of very walkable neighborhoods that also tend to have an abundance of nightlife.
I think it has gotten better since Uber/Lyft came about as well as younger people not being hesitant to take the subway (now open until 2).
Terrible driving in general is still the same - no signals, double-parking without hesitation, general craziness. On big holidays, there are a lot of drunk driving checkpoints but, overall, very little to no traffic enforcement.
Hit-and-runs are a really big problem.
I think the city is going through some growing pains as there as there are more pedestrians and cyclists on the road. If you are in those categories, you have to be very, very aware.
As a comparison, I was much more worried about drunk drivers when living in a rural area. Also, a recent visit to Santa Fe I saw at least 2-3 clearly drunk drivers, which my friends said is a huge problem there.