Celtics forward Marquis Daniels committed a foul prior to Marvin Williams releasing the in-bounds pass, meaning Atlanta should have had a free-throw attempt and still retained possession of the basketball.
Instead, the NBA officials ruled that the foul occurred after Williams' throw-in, and the Hawks essentially re-did the possession with the foul not harming the Celtics.
Atlanta trailed 81-79 at the time, and Hawks forward Al Horford ended up missing one of two free throws on the possession, icing the game and the series for the Celtics.
One extra free throw for the Hawks in the waning moments of the game completely changes the complexion of the series.
The NBA admitted fault, and here is their statement found here:
During the last two minutes of the fourth period or overtime, if a personal foul is assessed against the defensive team prior to the ball being released on a throw-in, it is considered an Away-From-The-Play Foul and the offensive team is awarded one free throw and possession of the ball. With 3.1 seconds remaining in the the Boston-Atlanta game last night, a foul was called on the Celtics’ Marquis Daniels after the Hawks’ Marvin Williams had released the ball and therefore the foul was correctly treated as a common foul and not an Away-From-the-Play foul. With that said, however, the replay shows that the foul on Daniels should have been called sooner than it was by the officials, in which case it would have met the requirements of an Away-From-The-Play Foul.
On another pivotal possession late in Game 6, Hawks forward Josh Smith took what appeared to be an inexplicable long-range jump shot.
But video, provided by SB Nation, clearly indicates both Horford and Smith were fouled on the play.
Smith starts out at far left corner of the screen, and then works his way to the basket where he is bumped by Celtics forward Brandon Bass. Prior to receiving the ball, Celtics forward Kevin Garnett wrapped both arms around Horford, another foul that should have been called.
The Hawks were, on the other hand, on the receiving end of two controversial calls that clearly affected the outcome of Game 6. There's no guarantee that the Hawks win Game 6 even with the calls, and even then there would be no guarantee that they would have prevailed in Game 7, but I would have liked to see it.