Salicylic acid is readily biodegradable in an aerobic environment. Most of it will be done in a few days.

I would, however, sprinkle it on rather than dumping the whole bottle in one place in the pile. It could inhibit some of the critters that make things into compost if it's too concentrated.

BTW, you didn't ask, but pharmaceutical expiration dates don't really mean that the stuff is necessarily bad after that date. It's just that the manufacturer doesn't promise that they will still be 100% (or 95% or whatever the standard is) effective after that date. It's a regulatory thing, they have to meet a certain minimum standard. Turns out a lot of things last years longer than that in dry form in proper storage. I usually don't worry about it until they're several years out of date.

More than salicylc acid there. The ingredients for chewability/palatability must be taken into account. Maybe good, maybe bad, maybe indifferent.

OP just said 'basic aspirin' so I assumed a compressed tablet, not chewable or flavored.

In any case, such ingredients are all presumably completely edible by people, so they are most likely compostable. But your general point is correct, if there are other ingredients, it might be good to investigate them, especially if a large volume is to be composted.