After Jesse mentions that Joey is 60 years old, Joey rebuts by saying he is "55ish." This is stretching the truth, because he was born on September 21, 1957, making him 58 years old at the time the episode aired
The only episode (in the spin-off) in which Nicky and Alex appear
There is a goof in this episode, for Jesse says he's been married to Becky for 28 years. However, that's inconsistent with the original show, given they were wed in season 4, having been married for four years by the end of Full House. Fuller House takes place 29 years later, making them married for 33 years, not 28.
Dedication to the mothers of Dave Coulier, Jeff Franklin, Bob Saget, and John Stamos
The original cast breaking the "fourth wall" (knowing that the Olsen twins would be watching), after referring to Michelle starting a "fashion empire"
Teri cheers Danny on during his rendition of "Wild Thing" – even though it's bad enough to chase nearly everyone else out of the room
A frantic Steve brings a pregnant Comet Jr. Jr. over for D.J.'s help as she is having trouble giving birth
Comet Jr. Jr. Jr. is born
In split-screen style, Joey, Jesse, Danny, D.J., and Stephanie recreate the scene from series premiere of Full House where they sing The Flintstones theme song to a fussy Michelle – this time singing to Tommy Jr.
Close-up of Comet Jr. Jr. as she prepares to have her puppies
Aside from baby Tommy, only the Gibblers are absent for Cosmo's birth, making it a family-exclusive event (Steve being part of the family in this case as her owner)