When they go to the Babbage's house, a cat runs by, and Lt. Randy Disher doesn't have an allergic reaction, nor did he at the end of Mr. Monk Bumps His Head (2006)(#4.11). But in Mr. Monk and the Missing Granny (2004)(#2.13) he says if a cat has been around within a year, he sneezes uncontrollably.
When Monk tosses the mail bomb into the toilet, he shuts the door. When it explodes, the door is clearly open and it's opened in the opposite direction.
About midway through this episode, Monk and Sharona are approaching the mansion on foot and the driveway is quite wet (as if there had been a heavy rain) but . . . in the background . . . the street is bone dry.
One of the main clues involves an unusually tied knot in a string tied around a package mailed to the murder victim. In reality, the U.S. Postal Service has not accepted packages secured with string since at least the 1980s because the strings cannot pass through mail-sorting equipment. Packages must be secured with tape.
A patient in a coma for 4 months would have a tracheostomy. A tracheostomy is generally performed after two weeks if a long term ventilation is predicted, as would be in this case.
The captain states that the bomb was mailed "three days ago." Even if the package had been mailed Priority Mail Express (overnight 2-day delivery), part of the plot was that the package had to be forwarded. This would have added 7-10 postal business days to the delivery time no matter the mail class. There is no way a package mailed "three days ago" would have been forwarded yet.
Monk "unplugs" a comatose patient, leaving him unplugged until his heart stops. Then, Monk plugs the machine in again and performs CPR, which "brings him back." But here the head of the bed is raised and the patient is on a mattress. CPR must be done with a person lying flat on a firm surface.
The ketchup bottle experiment to test the glue would've been meaningless. Even if the bottles were roughly the same weight as the packages, the surface area and materials being glued were completely different.
At the Babbage house when Randy states that ATF Agent is at 3 o'clock, he was really at the 9 o'clock position from Randy's vantage point.