When Sharona searches the pie for the bullet case, her hands are already tainted red from the cherry filling before she grabs into the pie. Her hands were probably already stained from a previous take.
When Lt. Disher is telling the husband to place the pie on the hood of the truck, he's pointing with his right hand. Cut to a front view and Disher is now pointing with his left hand and his flag lapel pin (always worn on his left) is now on his right lapel. The cut has been flipped.
As Ambrose's house is burning, firefighters are shown entering without Self Contained Breathing Apparatus. They would not enter an actively burning structure without SCBA.
When Ambrose tells his neighbor that you don't use flour to make chili, flour is a common thickening agent used in making chili. You wouldn't use a lot, but flour is by all means a common chili ingredient.
Monk says that because the killer's gun is registered, the casing would be easily traced. That would only alert the police that he owns a gun. His shell casings would still have to be matched to the killer's casings.
Casings can't be traced back to guns.
When Ambrose picks up the phone to call the police and the neighbor cuts the line, the sound "line busy" is heard. In reality, if a phone line is cut, there's no sound.
In fact, there is no "line busy" sound heard from the phone on the audio. The dramatic music is too loud to hear anything like that. The only mention of "line busy" is is in the subtitles, but that is a goof in the production of the episode.
Monk says that the possible murder weapon is made by "Lane and Western". This a made-up company. It only exists in the "Monk" universe. The gun that is used is more than likely a Beretta.