Upon consideration...
The biggest mistake of the decade absolutely has to be failure to back Mancini in the 2012-2013 season... at all.
At the start of the season, Mancini pleaded with management for big signings... at one point he made an important trip to Milan meeting with Thiago Silva and Ibrahiminovic, both players on the market and willing - and indeed did - transfer.
Instead of landing these marque players... we signed, at the last minute, and overpaying...
Javi Garcia
Matija Nastasic
Jack Rodwell
Soctt Sinclair
Maicon
Richard Wright
Mostly complete crap, though Nastasic did perform rather well in his first season for us.
Back Mancini, sign high caliber players, and we might well have won the 2012-2013 title.
Which is not to say that Mancini should have been our manager long term - his substitutions/tactics were frequently misjudged, and his man-management and lack of ability to get on with others - players, and management both - meant that a better manager was always going to be available.
Nonetheless.... the 2012-2013 treatment of Mancini is, I think our biggest missed opportunity of the decade.