Found errors in paper: What happens now? As second-year bachelor students, we “validated” a scientific paper from our university. We took the raw data, evaluated it independently of the original paper, and then compared it back to see if there was a difference. It had recently been presented at a conference but has yet to be published in a journal. The task was assigned as part of our course project work. We were more successful then we imagined: We found rather large errors in some of the calculations. This was very satisfying for us, although probably less so for the people who wrote it. 

It was a fair bit of effort and we worked more than the other groups. Each group were assigned different papers or projects, i.e. nobody else was working on the same stuff. It was not compensated or anything being university coursework.
We hinted at the problem to the authors weeks ago but only submitted our work the other day.

Disclaimer: I am completely inexperienced/unknowledgeable in this academia thing. I might be completely off here.

This has lead me to wonder however:


What will happen to the conference proceedings in questions? The paper with mistakes can still be found online.
Can (or should) we expect any credit for our work when they correct their paper? I know people acknowledge help with, say, a novel or computer program, but does the same principle apply to finding a problem in a scientific paper? Our would this have been caught in peer review later?
Certainly not saying we are going to do this, but do people publish counter-articles to papers with corrections?


The field is aerospace engineering.
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.