The elementary way to monitor the progress of a reaction is to use Co-Spot.
In co-spot TLC, you have to spot 3 spots with the capillary tube:
1) LR-Limiting reagent (Lowest equivalent in ur case it should be salicylic acid)
2) CS-Co Spot (Both reaction mixture and the Limiting Reagent)
3) RM-Reaction Mixture (from your rbf.)
Now compare your reaction mixture spot and the co-spot to see if the limiting reagent is present, if it is present, you can add more equivalent of acetic anhydride to push the reaction forward. However, if the limiting reagent has been consumed you may stop the reaction and do a quick work-up or purification (recryst.).
If the compound has conjugation system, you can use observe the spots under UV, otherwise please try other methods like Iodine staining or KMnO4 etc.