Found errors in paper: What happens now?
The very first thing you should do is notify the authors that you found errors. This serves two purposes:


Gives the authors the chance to correct their results and publish an erratum to their paper.
Gives the authors the chance to rebut your arguments in case it is you who is wrong. Since they are obviously familiar with the work they might be aware of something you have missed. It would be very embarrassing for you to publish a Comment pointing out a problem that doesn't exist.


Be extra careful and polite when notifying the authors about the error and give them the benefit of the doubt. If you are helpful they would and should acknowledge your help in the erratum or revised paper. Since you said they are going to submit the work to a journal it could be that they even offer coauthorship.

They might choose to ignore your comments or, if they disagree with them, not take any action. In that case you can submit a Comment to their paper, write to the editor, or write a paper yourself with the correct result. Some authors have a hard time acknowledging mistakes and some editors might be unresponsive about wrong results that have already been published, so you might hit a wall or two along this road.

Again, whatever you do, make sure it is not you who made a mistake before making any claims.