The letter i in Castle's WRITER vest is no longer dotted from being shot in Season 6 Episode 4 Number One Fan. The bullet hole has been shown in other episodes since then, although it is possible Castle had a new vest custom made.
When Castle goes into Jerry's old house in the woods, there are pictures on the wall and one of the pictures is of Esposito, Beckett, and Castle in season 2. But they didn't meet Tyson until season 3.