Aspirin is acetylsalicylic acid. When it's exposed to water vapor, the acetyl group comes off and combines with water to make acetic acid, which is the acid in vinegar [1].
This happens pretty fast. An open bottle of uncoated aspirin tablets can start to smell of vinegar in a day or two, depending on the local relative humidity.
If you smell vinegar when you sniff your bottle of aspirin, toss the bottle. Why? Well, the other hydrolysis reaction product (salicylic acid) removes the outer layer of the skin and is used, for example, to remove warts [2]. Not something you want in your stomach.
[1] http://www.kii3.ntf.uni-lj.si/analchemvoc2/file.php/1/HTML/S...