yes, i hear europeans do this. Buy a car in america, drive it for two weeks, then give it away or take to wrecking yard.
* Almost none of the 50 states have inspection any more
* insurance is required, perhaps your home insurance will cover it
* Urban areas in California require smog testing for 1974 or newer
* You will pay for one year's registration, and possibly can get a refund on unused months
* Police don't hassle cars much. Unless they look like street racers...
But not sure about non-citizen registration. Maybe you can get a 30 day reg or something. Perhaps a smog exemption too.
I hear Mexico does not care where it is registered, but requires insurance, and a Bond when you enter to ensure that you don't try to sell the car. Probably going to border towns it is not required.
By the way, Mexican border towns are considered dangerous the last couple of years due to the drug wars. A guy I talked to this summer from Tijuana said don't visit. But I've also heard that if you stay about of the bad areas, no problem. Don't stay til the bars close, that's when people get mugged.
Mexico and central america are very particular about illegal drugs. Even a little bit will land you in jail for months with a slow justice system. Earlier this year 80 year old man from Seattle was put in jail after his grandson took a photo of two teenage girls outside a store, and it took a congressperson to help get him out of jail. The grandson is still in the Mexican jail. So be on good behavior if you go to Baja California.
Story.