Requiem for Methuselah - S3-E19
Corrected entry: Mr. Flint grabs the Enterprise out of orbit and transfers it onto the table. We assume, because the ship is small, it doesn't weigh much. However, Star Trek canon states the Enterprise weighs 190,000 metric tons, size not withstanding. There's no way that small table could hold such a massive weight.
Correction: We have no idea of how the technology he uses works. If he can shrink the ships down to a miniature size and instantly put everyone in suspended animation, there's no telling if he can alter the weight as well. Not to mention the fact that if he has such advanced technology, he could have a table that's able to bear the weight.
Bishop73
The old "Fantastic Voyage" problem. There are only 2 ways to make something shrink - either you reduce the physical size, and the mass stays the same, in which case the Enterprise on the table now has neutron-star level gravitational pull, OR you delete 99% of the atoms and keep 1 out of every 100 (sampling), like reducing a bitmap image in size. And just like that image, when the Enterprise went back up to full scale, everything would be "chunky."