The Classic Plastic Club judges on the point system, and I believe they break that down into six categories: 1)Engine; 2)interior; 3)Chassis; 4)Paint; 5)Construction; and 6) Degree Of Difficulty.
When judging, if any one of those categories cannot be viewed (or viewed well), it results in a points loss. Many do display their models on a mirror, and also use something to raise the model. However, in all things being equal, the model that can be carefully lifted, may have a better chance of gaining more points, simply because the judge(s) were able to get a better view than a model that was limited by the view the mirror/platform offered. And don't forget lighting.
Again, we offer the option of checking a "Do Not Touch" box. Because I do not judge at contests, I do not know for a fact if one way has favor over another, but I do know it (each category) must first be well seen and visible to gain a high score.
I have been a judge and never had to pick up someone elses model the standing rule was you get the owner to pick it up if needed.
I think only once I had to have an owner pick up a model in a tie-breaker situation.
To be honest, and maybe it's not fair, but I don't care what the bottom looks like - really. I have a pretty good idea of the model over all from guaging what I can see: fit and finish, paint, assembly, and overall appearance, decals, and glass. I also look for anything special or that stands out - especially if there is something that makes me ask myself how in the world did the builder do that. A bunch of poorly added details doesn't go very far with me.