I think the dog tells us something informative. IMO it shows LE not seeing one thing, and looking for an outside-the-box answer.
What I believe it shows us
I think the later dog search is a great indicator of LE's thinking in regards to trying to figure out why the perp had come there. The perp was clearly there for some intended reason (shown by the costume, and the fact it was done on an inconvenient night with the rain). One obvious possible explanation for the perp's presence was to specifically do harm to MB. But if not that, then why would they have been there?
So the other obvious thing to consider is they entered to take stuff. But imo this tells us that they really couldn't find any evidence of a theft gone wrong. Nothing was taken, but things of value could have been. So, they wondered if the perp came to leave something rather than take something, since the perp was there for quite some time and took nothing.
And what would someone leave? A bomb.
The next group gathering, when a bomb could have been set to inflict much damage, was Wed eve. So they brought in the dog just to make sure that there was no bomb left on the premises.
And since they didn't find a bomb either, then why did the perp come there? One more indicator, if we needed one, that it was specifically to do harm to MB.