The tattoo shop is in Bayport, Long Island. In the book series, the Hardy Boys live in Bayport (in a never-named state).
Easter egg in opening credits: hula dancer figurine in Oliver's window is like the one on his car dashboard.
The car owned by Oliver Putnam (Martin Short) is a French Peugeot 504. This was the only Peugeot car offered in the US market in the early 70s and a rarity there.
Charles (Steve Martin) mentions he got crabs in Massapequa. That might be a joke to Alec Baldwin. Alec Baldwin and Steve Martin have a rivalry for most guest appearances on SNL. Alec Baldwin is from Massapequa.
Cassandra (in Greek mythology) was cursed to always be able to foretell the future but never be believed. Lady MacBeth (of the play Macbeth, by Shakespeare) was known for being scheming to the point of murder.