I too felt that season 2 was much better than season 1 because it focused less on bashing Michelle or Mary Kate and Ashley Olson, and breaking the fourth wall, and more about the show being its own despite referencing the previous series here and there. Regardless, the referencing of the previous series happens in half of season 2, it didn't seem as frequent as season 1, imo.
The writing has definitely improved, though it is as corny as a '90s ABC sitcom. While people had issues with season 1 being raunchy, I felt season 2 tone it down a bit as they don't reference Stephanie's boobs as often like the previous season. I did find it a bit hilarious that Danny had no issues with the way Stephanie dressed in the original series with the crop tops.
What was strange for me is how they gave Joey a family after implying that his character never married, yet alone had kids in season 1. I know they didn't flat out said that he was single in season 1, it was strange for him to visit the Fullers and the Tanners (first episode of season 1) without any mention about his family. Perhaps the writers didn't want the character to be a stereotypical man child so they rewrote the character as having a young wife and kids for season 2.