Aside from 07 where the patriots were unstoppable aside from the game that mattered most, they let legit opportunities pass them by in 06, 08, and 09.
The 06 implosion to New England
Going 8-8 in 08 causing them to have a lower seed in a year where Brady was hurt. They lost some stupid games that year to teams they had no business losing to. Having Pittsburgh at home instead would've made a huge difference.
09 the jets divisional game loss following an 11 game win streak. Again in the afc title game they would've met the team who's number they had during that timeframe and just beat in the playoffs the past 2 years in a row.
They blew some golden opportunities during that stretch.