The slight modification of the interior set of the McMillan's home provided a continuity problem. In season five's, "Aftershock", the mystery centered around a skeleton found in their brick fireplace which supposedly had been put there when the home was built. However, in at least the first two seasons of the show, their fireplace was of different construction and not made of brick, thereby belying the idea the skeleton could have been there all along.
There an inconsistently with the spelling of Commissioner McMillan's first name. In at least one early episode, the first name was shown spelled as, "Stuart," while later it was commonly spelled as "Stewart." Given that he is supposed to be of direct Scottish descent, it would more likely be that his name should be spelled as Stuart.
Police commissioners are administrators, not investigators. They would not have the time (and potentially lack the ability) to solve crimes. In fact, the involvement of the commissioner in an active investigation would likely be used by the defendant in any appeals if they were convicted.