It's fairly easy for well-intentioned mathematicians to make small mistakes in their reasearch that drasitically affect the outcome of a proof. The sorts of falsehoods discussed in this paper are a consequence of lying about the source material, or a severe lack of due diligence. So these fields probably have a lower prior for a falsehood in a paper.

But in the vast majority of cases, these small mistakes are caught by other mathematicians. This is because verifying a proof is easier (in terms of resources) than, for example, replicating a randomized control trial (with the necessary equipment and subjects).

Not necessarily. Most papers are only ever read by a few people, and even very well cited papers can contain errors which may not be corrected in public unless they significantly change the outcome (but which can make analogous proofs more difficult, as I found with a 2000-citation paper in my PhD's field (its outcome wasn't affected)).

It probably happens less often in mathematics, but it is not immune: in 1932, von Neumann "proved" that hidden-variable quantum theories are impossible, but his proof was amazingly flawed (he essentially assumed that an average of sums is equal to the sum of averages), and the flaw wasn't widely noticed until John Stewart Bell pointed it out in 1966 with an anguished quote that has become quite famous:

"Yet the von Neumann proof, when you actually come to grips with it, falls apart in your hands!... It’s not just flawed, it’s silly... You may quote me on that: The proof of von Neumann is not merely false, it is foolish!"

This is more of a mathematical physics example, but everybody in every field could stand to have a bit more humility and rigor.

maybe i am just tired right now but "average of sums is equal to the sum of averages"

is basically true 100% of the time-it is called the linearity of expectation and is a basic fact of probability.

Could you include the papers or provide a more detailed comment?

Sorry for the confusion, I attempted to simplify the issue for the sake of clarity but apparently only made it worse. You can get a more rigorous explanation of the problem here: https://arxiv.org/abs/quant-ph/0408191