What was your solvent system? And how large is your solvent reservoir?
I have found that with very small chambers and volatile mixed solvents, you can see a lot of drift from plate to plate just due to differential evaporation of the solvents. Dichloromethane is very bad about this. If you have larger chambers with no filter paper on the sides, it is possible that your vapor isn't always in equilibrium with your liquid, and you can see evaporation from the plate as it elutes which will also appear as a change in the Rf.
The best practice would be to always spot your product spots against a sample of the crude material - that way you can tell if the spots are just running differently under your conditions, or if you truly have a change on the silica gel.
Impurities shouldn't affect your Rf unless they are really changing the plate or the solvent properties. Traces of DMSO, DMF, water, or TEA can cause substantial streaking and spot movement, for example. Impurities from the reaction rarely do; they just show as an extra spot.