This is one of the few times Natalie refers to Monk by his first name, Adrian. For the rest of the series, she refers to him as Mr. Monk.
This is the only episode where the person who died was not murdered but simply killed in self defense. The investigation is about who attacked Natalie Teeger and why.
The Sea of Tranquility exhibit was inside the California Science Center at Exposition Park in Los Angeles, CA.
When Mr. Monk is brought into Julie's science teacher's classroom, Natalie introduces him as a professor from Berkeley (Science Department). This is, in fact, where Adrian Monk attended college.