Sparklefizz
The police may not have done a sterling job - we really don't know for sure - but the main problem has been THE PUBLIC - interfering, speculating, demanding to know everything, treating the tragedy like some Netflix series, taking selfies on the riverbank, acting like Poirot, hassling the family and trolling. It's been awful to watch.
The police didn't treat this as a crime scene as it was not considered to be one, but perhaps they should have taped off the area anyway (there are different types of tape for different scenarios) and not allowed the public to tramp all over the area.
Much speculation could have been avoided and it could have been handled much better (my opinion only). The police knew about the previous problems but they did not need to be divulged unless the family did so.