When Monk confronts Christine in the church, he mentions that she must not have told one of her previous husbands that she had been married before him because he was a deacon and he could not marry a divorced woman. Although this is no longer the case, at the time, a deacon who was not married when he became a deacon was not allowed to marry at all.
On the phone to Sharona, Dr Kroger attributes Monk's speaking gibberish to a shorting out of the "occipital lobe in the left hemisphere of his brain which controls the ability to speak and to form words." The occipital lobe is primarily the visual cortex and does not control speech or word formation.
When Rutherford is hit over the head with the bust, the fresh gash immediately has a 2-3 inch blood trail that does not flow any further. Bleeding head wounds typically flow freely in the earlier stages.
When Gail hands Monk the envelope, she tells him it contains the phone records he requested, but Randy didn't tell her what was in the envelope. Gail could have opened the envelope and seen what was in it, but she wouldn't have known that Monk requested the records.
During charades, everyone starts shouting out the category of Darryl's phrase before he even starts making the gesture for it.
When the cop says "Now please step back," it is clear that his lips are not moving.
When Sharona enters Monk's apartment just after the earthquake, the shadow of a boom mic can be seen to the right of the doorway and pulled up out of frame as she enters the living room.
After Sharona discovers Monk in his aphasic condition, she calls his therapist. He tells Sharona that the aphasia is centered around the occipital cortex of the brain. This diagnosis is incorrect. Aphasia happens mainly because of damage or stress to the brain's language center, Wernicke's Area, in the cerebral cortex. The occipital cortex is the vision center of the brain, and damage to this area typically leads to blindness or other vision issues.