Originally Posted By: Kestas
I agree. It looks like the table has a matte finish and the glass burnished a few spots to make them shiny.
I can't tell from the pictures, but if it's a satin or matte finish, then those spots are the result of "polishing" from the glass pads.
So, the marks are not stains, despite the thread title, and the fix is to bring the finish to an even sheen. So, rubbing out the finish is the fix. However, the first step (usually a 400 grit wet/dry, but 0000 steel wool could be used since this is an older/existing finish) can cut through a finish if it's old, or thin, or done too aggressively. The next steps are more gentle, if your desire is to bring it back up to semigloss, or even a gloss finish.
I found this article, and while it's for a new (not existing) finish, it's a pretty good overview of the process:
http://www.woodworkersjournal.com/Main/A...inish-5261.aspx
And I would start with the 0000 steel wool on this finish, there's a chance that those "marks" are also slight depressions in the wood itself, and so the wet/dry sandpaper would risk damaging the finish around those depressions, while the steel wool cuts less aggressively.