Are there any problems with that paper that would invalidate their conclusion that myocarditis is more likely in young men who get Moderna than young men who get Covid?

My biggest concern is the studies that have been comparing myocarditis induced by the vaccine vs. those with MIS-C from COVID-19 that show that they're not necessarily directly comparable - the vaccine-induced version is also milder.

It is elevated, but the implications of that depend wildly on things like case rates, as events/vaccine doses is static, and events/cases is dynamic. A conclusion reached in Sept., 2021 misses a huge upswing in cases in young men from Omicron, which while milder on a per-case bases has also caused a lot more cases (to use a gaming analogy, making better saving throws, but making a lot of them).

Do you have a source on the vaccine-induced myocarditis being milder? If that's true then it is indeed a crucial thing to keep in mind when interpreting these results.