Kim, the integrity of the structural elements need inspection certainly as I remember seeing some very tidy "tarted up" classics that under the surface were like Swiss cheese! Not only that, but as a trained welder made me shudder when I saw some of the botched repairs using Oxy-acetylene or worse, a MIG welder. An MOT would go some way to re-assuring the car is sound.
But also an inspection of the braking system, steering, bearings etc. A lot of the components that it's not obvious if they are failing, and in the "youth" of the vehicle would be picked up now by the service regime as well as the MOT. (Hopefully!) These can be some of the items that are just not checked by the owner unless some work in restoration are being carried out on them.