During the flashback, you can clearly see a Jaws movie poster in Hank's room. However, the story takes place in February of 1975. Jaws didn't premier in theaters until June.
Peg tells Hank that the school nurse told her that one could not get mono from sharing drinks. This is categorically false. You can contract mono if an infected person's saliva mixes with yours. Hank's story is plausible.