Notorizing DOES NOT make a rental agreement legal.
A Notary is not a legal expert or a legal authority.
The Notary stamp ONLY states that "John Doe" is the person that signed such and such document and that the ID was verified and signature witnessed by the notary.
THAT IS IT.
Understand that rental contracts are legal documents...and unless you are a licensed attorney, you cannot draw up a legal document unless you have a law license.
A notory is for when you need to protect against forgery.
I have rented apartments in three different states, and I've never had to get it notarized.