It comes up with an error "this application requires a version of adobe air which cannot be found"

Googling it finds that it may be an issue with the latest Adobe Air… https://forums.adobe.com/thread/2457852

I got around it by fully uninstalling Adobe Reader (not just moving to trash)

I also told OSX to open PDF files with Safari instead of preview as this makes DentalPlus open the PDF in the browser which doesn't have the issue.