The scene where the plumbing leaks and floods the bar actually has two major errors. First water does not and cannot come spraying up out of the drain in s sink unless there is an explosion in the drainage system which is not likely under these circumstances. Second, regardless of the size of the leak, there was not enough time for the volume of water flooding out of the kitchen to have leaked from the pipes.
The painting displayed on the computer screen which is "supposedly" the stolen painting over which the forgery was painted looks nothing like the image of the underpainting of the forgery. They are completely different paintings having only a waterfall in common so that painting could not be the one that was used.
Searching the museum is fruitless since neither Rizzoli nor Isles are art experts capable of spotting forged paintings that even an expert cannot do with only a cursory visual examination. Beyond that, there are dozens of art patrons in the museum so it is highly unlikely that someone else would not notice the discrepancies that Maura noticed within a few seconds of casual viewing.
Maura says they should look for paintings with a lot of blue in them. Finding flecks of blue paint does NOT lead to the conclusion that the painting was mostly blue. In fact, it does not indicate the blue paint even came from a painting.
Korsak spots a burned wire in the fireplace and immediately says it is the wire from the stolen painting with absolutely no evidence to support his claim.