Roger wears a t-shirt that reads Patton Vocational High, but he doesn't get a job there until a few episodes later.
When Fonzie starts to read aloud the book Barbara gives him, he opens and folds back the cover of the book and starts reading the first page of the story. Such books of several pages before the beginning of the story (like the copyright page, the table of contents, etc.), so he should have flipped past several pages before he started to read the book.
All of the women wear low cut bikinis common in the 1970's that never would have been allowed in public in the 1950's.