In table tennis, on the rare occasion when the ball makes it over the net but hits the side of the table rather than on top (which is pretty hard to counter), Is this a valid point?
International Table Tennis Federation (ITTF) rules in regards to the table go to 2.01 ("The Table"), or playing surface are fairly straightforward and short. A ball is in play if it touches any part of the top of the table.
2.01.02 The playing surface shall not include the vertical sides of the tabletop.
Therefore, anything not considered the "top" surface of the table would be out and the point would then end. So in your case, I assume someone went to the side of the table to return a hit, and it struck the side of the opponent's table (or as the ITTF refers to it "the vertical sides of the tabletop"). This hit would be out.