If I'm going to use a potentiometer as an adjustable voltage divider, does the tolerance or resistance matter?
If you are just taking the voltage into a high-impedance load, then the value of the pot doesn't matter at all.  1k and 10k pots will both give 2.5V at 50% rotation.

It is a common pattern in electronics to make things ratiometric so exact values don't matter.  In this case, the tolerance and temperature coefficient of the pot is completely canceled.