which is correct? some advertisement or some advertisements?

You probably want "some advertisements." If someone were to say "the job is to audit some advertisement," in the singular, it would mean that they are referring to a specific advertisement, but hadn't troubled to identify it more accurately, and there would be an implication of seeing the ad in a dismissive light. By saying some advertisements, you are saying some unspecified ads, but the statement is value neutral, and would be taken as a description of the job as planned.

Thanks

The job is to audit some advertisement [in] on A2K to ensure commercial behavior will not hurt user experience or affect any academic freedom.




No, it wouldn't mean that. It might, I suppose, if there was that context. It could mean "one of the advertisments", "the one advertisement that you choose to audit".

[I'm a little puzzled as to the use here of 'audit' and 'job', Ori.]



Equally false, unless there is a context that I'm missing, which is possible.



Equally so, by saying "some advertisement [no 's'], you could be saying what I described above.