In season 3, Jesse states that he went to Nebraska with Becky on Valentine's Day. He even gives into going to see her family that Christmas. So Jesse would have met Becky's family on more than on occasion.
As Stephanie is reading the letter from Uncle Jesse, she is holding it far away despite needing reading glasses in "Stephanie Gets Framed".
Jesse says he never skydived, but he did according to him in "Daddy's Home".
When Danny wakes Michelle up to ask her about Jesse, the way her hands are crossed changes between shots.
Jesse states that he took all the skydiving classes but never actually jumped. Even with all the training completed, you cannot go up in a plane on your own with a pilot of your choice and jump without an instructor. It is required to complete a certain number of jumps with a trainer before you can jump on your own.
When Howie is jumping on the bed in Michelle's room, he says he's Raphael when he's actually Donatello since he's wearing the purple accents of a Teenage Mutant Ninja Turtle.