How can you qualitatively tell when the hydrolysis of aspirin is over?
First I was thinking that maybe a chemical indicator could be used, however the pKa values of all three components are relatively close to each other (especially aspyrin and salicylic acid). It might still be a bit of a help to stick a pH electrode in the system and observe the change - however, this is not exactly something you can see easily.
Another thing that came to mind is that salicylic acid (as all phenols) will form a colorful complex with Fe(III). However, the appearance of the red-ish color will only tell you when the reaction has started, since it's borderline impossbile to observe that the solution is not getting any darker anymore. Again, if you have some machinery, you could stick your solution into a cuvette and put it in a photometer.
Apart from the two ideas above, I don't really see an easy way of observing anything.