There are three pivot points and one sort-of-support point that you can check for looseness and wear. In all three cases you can make some adjustments.
1. The plastic pivot ball on the shift lever itself. This is sandwiched between the halves of the shift lever mount that fastens to the center tunnel with three capscrews. Disassemble this and check that the black rubber collar and white plastic collar inside are intact.
View attachment 58352
2. The clevis at the base of the shift lever. Check for loose nut and bolt, or wallowed-out holes in the shift lever and/or shift rod.
View attachment 58353
3. Lollipop--already covered by other posters.
4. The boot that seals the opening at the back of the center tunnel through which the shift rod protrudes does provide a minor level of control and support, as described by Dr. Jeff above. Check to see if the boot is missing, torn, or otherwise deteriorated.