Your interpretation of the actions of the police as incompetent are probably mistaken because of a failure to appreciate the true goals and motives of the police here.
This story makes me pause and consider cui bono.
It appears the mother went directly to the principal rather than the teacher. The recording and transcription also seems to cast the teacher in a poor light. So it would seem the initial complaint was as much against the ineffectiveness of the teacher as it was against the bullying itself. It seems the mother had discussed this issue with the teacher previously... repeatedly.
Next, why in the world would the school administration involve the police at all? Do they truly have no ability to manage things at this school without this? No, it seems blatantly clear the goals and motives of the school administration immediately shifted to DAMAGE CONTROL. They never had any concern over the bullying issue itself. The teacher had a reputation to defend. The school was in an adversarial role from the beginning - fighting the complaint, not addressing it.
So... why would the police allow themselves to be used in such a fashion? Because using antiquated wiretapping laws to prevent citizens from recording the actions of police is a rather favorite interest of the police these days. The police had no intention whatsoever from the very beginning to "address the problem" if by that you meant the bullying. They eagerly jumped on board here because they were handed, on a silver platter, a wonderful opportunity to make a loud example of someone to remind everyone they shouldn't DARE record the police. Failing back to disorderly conduct wasn't inept. It was entirely in line with their goals.
Soo... what SHOULD they have done? I am sympathetic with the idea of tossing the video immediately into the Net. But other than the PR or novelty impact, how would this have changed anything vis-a-vis the Wiretapping charge or the actions of the school? I wonder what would have happened if instead, the mother asked for a meeting with the teacher and principal and sat down to discuss these issues, alluding to the transcript only if necessary. At the very least she might have gotten the principal to consider addressing the bullying issue by properly managing the teacher rather than running straight to the school's attorney.