You'd be better off with written affidavits from each of your adjacent neighbors that can hear the noise. Also worth noting, is that obvious drug use (given the "tweaking" comment) is expressly part of the nuisance statute use in Cali.
Also, the walls being thin may simply mean that the unit is not comfortably habitable, and that you had no way of knowing that before moving in; particularly with loud neighbors. Unlike many other states, you do have options here - you're not required to live somewhere that is insanely loud even if the landlord doesn't have an easy fix to keep you in the unit. If the walls are paper thin, and the neighbors can be heard as though they're in the next room - and this is causing you distress - you should be able to get out of the lease.
Moreover, why on Earth would the landlord hold you to the lease to begin with if you tell them your plans to hold them accountable? Most landlords will look at the situation and realize they're going to lose money rather than make money by trying to force you to stay.
I guess the only question I'd have is, how desirable is the location and how fast do you think they can lease your unit? If they can replace you in a reasonable period of time, then I don't think they'd have any issue letting you out of the lease without any litigation.
Alternatively, you could go in, as part of an attempt at an amicable resolution, tell them you cannot live under these conditions anymore, and that you're willing to let them show the unit while you continue to rent for another 30-60 days, and that you only need two weeks notice to leave if they find a new tenant. Most landlords will appreciate that and will immediately list the unit for rent rather than try to hold you to the lease.