How much of a paper does a reviewer fact-check?
I'm afraid there is no one-fits-all answer to your question. It highly depends on the tier of the conference. There are some that examine more into the work than others.

However, the level of scrutiny in CS conferences are generally less than that of a journal of comparable reputation. This is because, such journals go through multistage reviews and edits before the final print is published. Most conferences look only into the conceptual matter and usually have insufficient time to exhaustively implement and test the proofs of each of its candidate papers with limited reviewers.

Having said the above, there are some journals that scrutinize lesser than some conferences. Like I stated before, it all depends on the tier and reputation of the publisher.