You have to pick:

Wouldn't we all just eventually become dogs? The jam would just get worse and worse and then every single driver would just be a dog. Or do we still have our brains? or does leaving the car count as ending the jam?

Well, if the traffic in front of you clears you turn back, so the people in front can always move, thus allowing the traffic jam to ultimately end. It shouldn't really be that much different than a normal traffic jam ... except that while you're waiting you're a dog ... so who knows what you'll get up to during that time.

I guess the jam might clear a little more slowly because each person has to climb into the driver's seat from whatever chew toy they were playing with in the back.

Also, you would never want to drive with the windows down, because you don't want to escape.

@ DangerStevey
I assume you DO have the MIND of a dog during this time, not just the body ... otherwise it's kinda pointless. In that case the only issue is making seats that are comfortable both for humans and dogs, since in all other respects its not really different that waiting in traffic normally.

You know what they say...never leave a dog in a car, they can't survive the heat. So no thanks.

@andemon: Good point - make sure to always have the AC on

It'd be annoying, but prosthetics do exist that would restore basic functionality, so I would be able to walk, at least somewhat.

Failing that, a wheelchair. Could be worse.