Often, the quality of a Drosophila lab can be judged by the quality of the stocks kept within. If you are using Drosophila as a scientific tool, it is never acceptable to have mites present in your cultures.
Mite infestations can spread impressively quickly, but are actually easy to get rid of.
To remove mites, simply rapidly turn over stocks. The mite life cycle is longer than that of the flies, and they also normally hang on to the vials/bottles more effectively. If you turn young flies over into vials with mite proof seals (compacted cotton wool, or flugs) around five times in seven days, the final vial should contain only flies. After two weeks, the vial can be checked for mites. If none are present, then the problem is solved. If mites are still present, rinse and repeat, however, I have never experienced an instance where this method did not work first time.