In the flashback at the beginning, Trudy mentions that she has a busy day including picking up medication for Ambrose. In episode #2.11, "Mr. Monk and the Three Pies", Ambrose reveals to Adrian that Trudy was out that day because he had asked her to pick up cough medicine. Adrian would have known if the events played out like in the flashback.
In episode #3.7, "Mr. Monk and the Employee of the Month", MegaMart security guard/former SFPD office Joe Christie tells Sharona that he was there when Adrian got the call that Trudy had been murdered. Joe Christie was not in the scene in the finale episode, though he was accurate in saying Adrian was laughing when the call came - and it was the last time he ever laughed.
Judge Rickover mentions in Part II that he is a federal judge. There is also a mention of the fact that he is on the Court of Appeals. However, Captain Stottlemeyer has the judge sign off on a search warrant. First, a federal judge would not sign a search warrant for a local homicide investigation. A state judge would take that role. Second, a Court of Appeals judge, state or federal, would never be in a position to sign search warrants.
The goof items below may give away important plot points.
Errors in geography
** Judge Rickover discusses having to commute to Sacramento due to his nomination to the California Supreme Court. This becomes an important plot point later as to why the judge would never sell his house (presumably located in the San Francisco Bay area). However, the California Supreme Court is actually located in San Francisco, CA. The judge would never have to move or commute to Sacramento for this job.
When they realize that Joe Kazarinsky poisoned Monk's stuff at the grocery store the doctor specifically says they will test "every item" on the receipt. Yet in the second half Natalie realizes that the wipes were poisoned. If she bought them at the grocery store why were they not tested? If they weren't purchased at the store when were they poisoned by Kazarinsky?