Ainge did not let Tony Allen walk. He offered Allen more money than the Grizzlies did. TA wanted a bigger role and didn't want to play behind Pierce and Ray. That's not Danny's fault.
I'd say the last bad move Danny made was signing Jermaine O'Neal. I'd say most, if not, all of Danny's bad moves were explainable when they were made. They just turned out a lot worse than expected.
That's how I remembered it too, and we remembered it correctly:
The Grizzlies stole away Allen from Boston in the summer of 2010 with a meager three-year $10 million contract, a deal that gave them the Celtics’ perimeter stopper in his prime.
The loss of Allen via free agency can’t be entirely blamed on Ainge. Memphis offered Allen a starting job, something Ainge couldn’t do with Paul Pierce and Ray Allen firmly entrenched in the starting five. Still, Boston likely would have been able to make up for reduced playing time with dollars, and Boston’s offer was not sufficient enough in Allen’s eyes to stay in Beantown.
http://boston.cbslocal.com/2015/05/06/robb-tony-allen-the-one-who-got-away/
Edit - I always thought the money was the same, just Allen wanted a bigger role.
Just to pile on, I also remember it the same way as MJohnnyBoy does: as Tony Allen leaving primarily to get larger role, one Danny couldn't give him on a team with Ray Allen and Paul Pierce. And that's how Tony remembers it as well:
http://espn.go.com/boston/nba/columns/story?id=6560546&columnist=forsberg_chris"Ultimately, it was the way [the Grizzlies] embraced me, the way they reached out to me and let it all out," said Allen. "They let me know I was needed. In Boston, I was kind of overshadowed by those guys -- Paul Pierce and Ray Allen."So, if Danny made a "mistake" here, it's one of not somehow magically carving out a bigger role for Tony. But it's hard to see what exactly Ainge could have done to accomplish that.
Note that there was a ripple effect from that (which the above Forsberg article talks about): Because Ainge was unable to retain Tony, he had to sign Marquis Daniels to be the back-up wing. 'Quis played well, but as we all know, suffered that horrible freak spine injury the following January. That put the Celtics in a bind with no back-up SF behind Pierce (along with a growing pile of injuries at Center with Shaq, Perk, Jermaine & Semih all injured). That put extra pressure on Ainge to make the Perkins-Green deal because it shored up depth at both positions.