95 SL! Loose Shifter!

95 Saturn SL with a manual transmission. first the shifter was flopping around and wouldnt go into gear. took it apart and found the cable was broken off the shifter. put a new set of shifter cables, now it goes into all gears fine except theres a little trouble getting it into reverse everynow and then. but it still flops around. you can put it in first and move the shifter side to side just as if it were in nuetral? took the cables off the shifter and everything works fine. it pulls the detent lever as it should. if you pull the cables from the transmission side, it pulls the shifter as it should. everything works right, it just still flops around. I tried a new shifter because I thought maybe it was worn but it still does it. Any suggestions? Possibly something internal to the transmission? Let me know.