In this episode, Joey states that he has never had the chicken pox and gets them later in the episode. However, in episode 4.7, Colonel Gladstone talks about watching cartoons with Joey when he was three and had the chicken pox.
When Jesse comes downstairs sick, D.J.'s spoon jumps from her bowl to her mouth a little too quickly.
D.J. states that she's looking forward to her very first Slumber Party. D.J. is 10 or 11 years old during the first season. However, in the season 4 episode "Slumber Party" Stephanie mentions that D.J. already had her first Slumber Party at age 8 together with pam.
Michelle could still catch the chicken pox just being in the house. Chicken pox is an airborne disease and can also be transmitted through infected items such as clothing. Michelle should have been out of the house until everyone got better.
When Joey is goading Jesse about the "red throbbing strobe light on (his) nose" when they're trying to see which one of them scratches their itches first, Dave Coulier slips up and says 'ssthrobbing'
Joey says that he is immune to chickenpox since he never had it which is false. You can only be immune to something if you have been exposed to it. Even then, if someone has had chickenpox, he or she can still develop shingles later in life.