How much side to side movement? this issue is probably in the linkage, as checking the mounting bolts to the shifter is easy enough, just take the boot off and check the 4 bolts. If they're tight, I'd take 'em off and look at the ball on the bottom of the shifter and then the arms they fit in to. If you can see down in there for any debris or broken pieces, problem solved. If you can't, a more invasive job is ahead of you...