That would cause a wobble. Was it on the rear? Rear wheel out of true or balance is often the cause of a shudder between 60 and 70 mph.

Not sure if it would be a failure even if he had spotted it. The actual wording of the reason for failure is " a wheel badly damaged, distorted or cracked, or with a badly distorted bead rim" and it would depend on whether he thought it was badly damaged or merely damaged (or if he also sells alloy wheels).

Yep, rear passenger side. I won't be mentioning it if I don't already have a replacement wheel to hand for them to swap the tyre onto - it has held air for the 6 months I've had it so I don't want them potentially noticing and failing it on that after sorting the rest of things out. I'll get it replaced just as soon as I can get a wheel here, certainly not leaving it and hoping for the best.

A wheel refurbisher will be able to repair that. I have not long had an alloy wheel repaired (not a p38) and it was worse.
My alloy wheel had to be welded and ground off.