I just wrote this, and I realized it might be useful more generally:
The article looks reasonable to me–but I just did a shallow read and didn’t try to judge whether the conclusions are correct. My main comment is that if they’re doing a Poisson regression, they should really be doing an overdispersed Poisson regression. I don’t know if I’ve ever seen data in my life where the non-overdispersed Poisson is appropriate. Also, I’d like to see a before-after plot with dots for control cases and open circles for treatment cases and fitted regression lines drawn in. Whenever there’s a regression I like to see this scatterplot. The scatterplot isn’t a replacement for the regression, but at the very least it gives me intuition as to the scale of the estimated effect. Finally, all their numbers should be rounded appropriately.
Feel free to cut-and-paste this into your own referee reports (and to apply these recommendations in your own applied research).