Is it ethical for a part-time professor to use his position for other interests? There is a professor who works part-time at a university as a moderator of one of their student groups. He does not teach any actual classes but spends a hugely considerable amount of time with the members of the group outside of class hours.

Is it ethical that he uses his position to scout between those members for a company in which he is either a founder or a senior-level position (currently cannot recall which). He does not offer them jobs but instead constantly pushes and offers them to become "interns" with no pay, bad hours, and extremely heavy workload.

I'm not very well versed in business ethics but this sounds very wrong to me, and something of a conflict of interest.

Would the university have grounds to officially respond to this such as sanctioning him? I know that this professor was previously warned to stop doing so but nothing official/major was ever done despite him continuing to do so behind the administration's back.
As you remark, it is probably not okay, although it is always a fine line to draw: it's ethical (and highly encouraged) for a professor to help students procure good jobs and/or rewarding experiences outside the university (where “rewarding” covers not only monetary gains, but also experience learnt, etc.). He can do that through his network, and first and foremost in that network is the company he knows best. However, it is not ethical for him to abuse his position at the university and the student–professor interactions to the good of his own company.

Now, how active are universities in taking action against such behavior? It probably depends on the field, the country, the local situation and power of the professor, but in most cases I would say they will be willing to close their eyes, and it would really take a lot of evidence and someöne pushing them very strongly before they take disciplinary measures.

If you want to do something about it, discuss it very openly, and very calmly, with the director of your program, the students' representatives, the dean or departmental chair, etc. And document everything in detail.