I think we would all agree that the humour on Full House changed over the course of the series.
As I see it, the humour on Full House divides into four periods. Others may not agree with this.
Season 1
The humour in season 1 is relatively bland compared to the rest of the series, but does introduce a few of the running gags that were in the series.
Seasons 2-4
The classic period of Full House humour. This period includes the largest share of the well known catchphrases ("How Rude!", "You Got It Dude!", "Have Mercy", "Cut It Out", ect.). For the girls it has most of the classic DJ/Steph insult humour, a lot of the Steph/Kimmy insult humour, and Michelle's "cute" humour. For the guys it has most of Joey's classic jokes, as well as the running gags about Danny's neatness, Jesse's Elvis obsession, and his hair.
Season 5
The humour in season 5 is a transition from the humour of the early years of the show, to the humour of the later years. Joey's classic jokes are gone. The only catchphrase Stephanie has left is "How Rude!", and even this is de-emphasized. Michelle's "You Got It Dude!", phrase is de-emphasized, and "Oh Puhleeze!" becomes her new catchphrase. Michelle's "bad girl" humour, introduced in a couple of episodes in season 4, takes off. The Steph/Kimmy fights become fewer but more intense, and the running gag about Kimmy's foot odor problem takes off. The DJ/Steph insults largely dissapear. The running gags about Danny's neatness, Jesse's Elvis obsession, and his hair, continue.
Seasons 6-8
The final phase of Full House humour. The number of jokes decrease, and a much greater percentage of the jokes are scene based. Most of the catchprases are gone, except for Michelle's "Oh Puhleeze!", and Jesses's "Have Mercy!" and "Watch the hair". Steph and Kimmy still trade insults, but they don't yell at each other any more, and they cooperate on a few occasions. The running gag about Kimmy's foot odour problem continues through season 7. The running gags about Jesse's Elvis obsession die down, but the Jokes about his hair obsession become more exagerated. The running gag about Danny's neatness is de-emphasized.
I could go into even more detail, but I'll leave it at this for now.