Not addressing multiple hypothesis testing problems.

Just because you aren't performing a t.test on 1,000,000 genes doesn't mean you're safe from it. FI recently read a paper specifically about the pervasiveness of this problem in experiments, titled Multiple hypothesis testing in experimental economics and it was quite a good read. This issue notably pops up in studies that test an effect conditional on a previous effect being significant. Often in experiments the authors identify a significant effect of something, and then conditional on it being significant, then perform further tests to better understand it without adjusting for that procedural analysis approach.

Not addressing multiple hypothesis testing problems.

Just because you aren't performing a t.test on 1,000,000 genes doesn't mean you're safe from it. One example of a field it notably pops up is in studies that test an effect conditional on a previous effect being significant. Often in experiments the authors identify a significant effect of something, and then conditional on it being significant, then perform further tests to better understand it without adjusting for that procedural analysis approach. I recently read a paper specifically about the pervasiveness of this problem in experiments, Multiple hypothesis testing in experimental economics and it was quite a good read.