Here's my tuppence.
Registering. The first one I registered was fairly straightforward. Get it MOT'd, get an age verification from IMPS, MVT or any other relevent body and go to your local DVLA office. Fill in form V55(I think) and give all paper work in. They booked an appointment for me to bring the Jeep over for an inspection and that was it. Reg number and tax disc given straight away. The one I've just done was even easier. I took all paper work and a selection of photos and it was done there and then.
MOT's. I've never had a problem here. Some MOT centers that don't see vintage vehicles could be problematic. The best thing to do is find a Jeep owner close to you and find out who they use or if you already have a center you use have a chat with them.
Regarding common failures. Have the brakes well adjusted and there shouldn't be a problem. Wheel bearings and ball joints are easy enough to check as are the steering linkages. Likewise check your lights are all OK.
Scams. I guess it would be people advertising a hotchkiss as a wartime jeep. There's nothing wrong with the Hotchkiss, but if you specifically want an MB or GPW then that's what you should get.
Rust. Hat channels, floors and inside the toolboxes are the usuall spots to look at. Everything is repairable and parts are readily available. It just depends how handy you are or how much somebody would charge you to do the work. Keep an eye on Nick Johns' post as he's replacing some hat channels.
I'd recommend going over to G503 forums and having a read through there. Join up and ask any questions. That's what I did and it was a great help. Without it I'd have been stumped on some things.
Hope that's of some use. I'm no expert by the way.