What do you think it would be reasonable to expect me to have, if in fact the article is wrong or dishonest in some way?

I am not a virologist or cardiologist or any other sort of medic. I have not gone to Israel and interviewed the people they worked with. I am guessing the same is true of you.

So what can I do? I can look at whether the authors seem reputable (answer: probably? -- the corresponding author for this paper seems to be somewhat conspiracy-theory-ish on this particular topic, but since the question at issue is roughly speaking whether he's found an actual conspiracy that doesn't seem like a good reason to dismiss what he says). I can look at whether the journal seems reputable (answer: not incredibly so, it seems to be publishing quite a lot of junk). I also note that there's a note attached to the paper saying that something about it is disputed and they're still discussing with the relevant parties; that could indicate a real problem or it could just indicate that anything to do with COVID-19 vaccines is likely to provoke controversy.

I could also read the paper. But, again, I am not an expert in this field; if it looks good, I could easily be missing subtle errors (accidental or deliberate); if it looks bad, I could easily be missing subtle reasons why the things that look wrong to me are actually right.

My reaction to a quick look at the paper, as a mathematician who doesn't know much about vaccines or viruses or cardiac arrests: I'm not going to try to redo their analysis, but the graphs suggest that if there's anything here it probably isn't much; the matchup they say they see between vaccination and emergency-service calls for cardiac arrests is not obviously any bigger than the random noise in the latter. Maybe sufficiently clever analysis can make it clear whether it's signal or noise, but figuring out whether their analysis is sufficiently clever (and sufficiently robust, and done correctly) seems like way more work than I am interested in doing on this.

(Also: even if the most alarming conclusions anyone could draw from the data are correct, the number of adverse events here is still really small compared with, say, the number of deaths from COVID-19. The paper chooses to describe it as "a 25% increase" but that's from a baseline of "hardly any". The fatality rate of COVID-19 would need to be a lot lower than it is (even for the age group they're looking at, where it's relatively low) for this effect, even if real, to make the vaccinations a bad idea. Of course it's still an interesting question whether getting vaccinated against COVID-19 can cause heart trouble, and if so how, and if so whether there are ways to make it happen less. And it might (though it's not altogether obvious[1]) be worth warning people getting vaccinated to be on the lookout for signs of myocarditis. Reminder: you posted this link in response to something asking for evidence that myocarditis after mRNA COVID-19 vaccination is "a much, much bigger problem" than blood clotting after adenovirus-vector COVID-19 vaccination. It doesn't look to me as if the numbers bear that out even if the effect claimed in this paper is entirely real.)

[1] Because giving this sort of warning may increase stress, which is also not great for your heart.