Watching this show again lately on Nick @ Nite, it's kind of hilarious how much of an unintentional of a period piece (as TV Tropes likes to call it) this show has become for the late '80s early '90s. Off the top of my head (I think Nick@ Nite is right now into the 1989-90 season, which would be the third season):
*Posters of "Faith" era George Michael in DJ and Stephanie's room.

*The obnoxious boy that DJ babysits mentioning Teenage Mutant Ninja Turtles, when the original (1987-1996) animated series was at the peak of its popularity.

*Danny having DJ "swear" on a teenypopper magazine cover of Fred Savage (when he was on The Wonder Years).

*An instrumental version of Bobby Brown's "Every Little Step" as well as Madonna's "Crazy for You" playing at DJ's 13th birthday party.

*Stephanie clinging to Danny's ever move after an huge earthquake in San Francisco. This was obviously done in reference to the Loma Prieta earthquake that came before Game 3 of the 1989 World Series between the San Francisco Giants and Oakland Athletics. In the same episode, Stephanie asks the female therapist, if she had a Nintendo GameBoy. Ironically, ABC, who was broadcasting the World Series aired an episode of Roseanne and later, The Wonder Years in the immediate aftermath of the earthquake instead of Full House.

*DJ and Kimmie singing Paula Abdul's "Straight Up" while doing their homework in the episode where Stephanie accidentally drives Joey's car into the kitchen.

*Joey going on Star Search (which was the American Idol, America's Got Talent, or X-Factor of its date) w/ Ed McMahon.

*Candance Cameron's big, teased hairstyle around this period. This of course, came after John Stamos' epic mullet during the first season.

I remember all of those and I think that having those obvious 80's references is what made the show so great! I remember in one ep I think Jessie was thinking about moving out and he tells Joey "Remember that show My Two Dads? Two is all you need!"