The most common and obvious example is image duplication. This is used to invalidate large numbers of paper (I was absolutely shocked at the observed rate of image duplication). I am not sure I would call that a model.

The next example I can think of- I am not sure it qualifies. I read a paper where they deleted one gene at a time in yeast (it has 6000 genes) and determined whether the mutated yeast could live or not. For each gene where the yeast died, they added that to a list of "essential for life" genes. The paper concluded they had found some interesting proteins that should be studied. I read the paper and the first thing that sprang to mind, are any of these genes overlapping? Because we know (somebody already demonstrated in a lab) that genes do overlap (which is truly weird!)

I wrote a script and showed that every gene they reported as essential for life overlapped an already known gene that was essential for life. I wrote the authors, who never responded, but wrote a followup paper where they acknowledged they probably had a high false positive rate due to overlapping genes with known fatal effects. My guess is you'd say that either I used a model (existing literature) or I compared against the world, but realistically, what I did was trivially come up with a better explanation than the authors. T hat's what I want LLMs to do for me, and it seems like the direction LLMs are going will fulfill my desires.