Waht to do about my wobbly side table?

Your FLOOR is the problem. I an willing to BET that I can take ANY table and position it SOMEWHERE on your floor and it will wobble. I am also willing to bet, but not as much, that I can position the table you have somewhere on your floor and it won't wobble. This is true for EVERY 4 legged table and EVERY floor. I would find rubber shims to place under one of the legs to stop the wobble.