I would argue it could be appropriate to contact this professor. In general, it is great when you can work with the original author to make sure that you both understand the points of agreement, and collaborate on a future paper. When authors are willing to do this, it is much more efficient and pleasant than dealing with criticisms at the referee stage. When a new collaboration happens, it can lead to a much better paper! My best-cited paper happened because of something like this when I was a graduate student.
An example of this happening recently in the field of olfaction research:
You need to perform significant "due diligence" before you hassle a professor about potential errors. You are asking them to devote a lot of time and effort to your criticisms, and take seriously the possibility that you are right and they are wrong. If you list three potential errors, and the first one is something where you show a trivial misunderstanding, they might not devote time to the second and third. Here are some steps you can take:
Make sure your advisor agrees with your analysis of the mistakes.
Double-check to see if the other research group has addressed this point - either in a correction to the paper, a note on their website, or in a later paper on the same topic.
Ensure your email is as clear and polite as possible (again, your advisor should give you feedback on this, to make sure your points are coming across clearly)
If the errors are simple typos / potential misprints that don't affect the conclusion, don't make that the major point.
Edited to add: It also helps if your advisor knows something about this high-profile professor. Some people are very hostile to any criticism, or just don't talk with anyone below their "level." In my successful collaboration, my advisor knew the other professor, at least to say hello to.