Our Very First Show, Again - S1-E1
Continuity mistake: When DJ is talking to Steve in the kitchen, the calendar in the background for chores changes between shots. (00:23:00)
Continuity mistake: When Jesse and Becky first arrive at the Fuller house, in the closeup Becky's left hand is holding out the duffel bag (similar pattern color on her shirt) in front of her, as she and Jesse poke their heads through the doorway, but in the next wideshot it's her right hand holding out her black and white suitcase in front of her.
Continuity mistake: The shape of the staircase in the living room is slightly different to the original one. In Full House, the lower half of the stairs before the midway landing was shorter (roughly 5 steps) and the upper half was longer (about 7 steps) where as in Fuller House, the lower half is now the longer section (about 7 or 8 steps) and the upper section after the midway landing is shorter (roughly 5 steps).
Trivia: D.J. throws a life buoy onto a man which says SS Papouli on it. In Full House, Danny buys a boat and names it this in memory of the family's beloved Papouli.
