This paper is being pitched in media accounts as evidence that COVID-19 causes heart irregularities in half of those infected.

I'm skeptical. https://academic.oup.com/ehjcimaging/article/doi/10.1093/ehjci/jeaa178/5859292?searchresult=1

My sense is that there must be selection bias at work here. It's a prospective study, but the inclusion criteria involve an electrocardiogram.

Can someone involved in clinical care confirm or refute my suspicion that this strongly selects for individuals with cardiac problems?

To put it less gently, one might summarize the paper's findings not as "COVID causes heart problems" but as:

"Among patients with severe enough COVID symptoms to require hospitalization, when physicians suspected there might be heart irregularities, 50% of the time there were."