Late in Game 6 between the Hawks and Celtics, Marquis Daniels fouled Al Horford away from the ball. After some discussion, officials determined that the foul happened while the ball was inbounded, so the Hawks were given the ball side out with the Celtics having a foul to give.

It turned out to be a critical call, as Horford was fouled on the next play and missed one of two.

The NBA now admits the officiating crew made a mistake with the call. Per a league release:
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.
What that means is that instead of the Hawks having the ball side out, they could've selected their best free throw shooter to shoot the one attempt, then had the ball down one with 3.1 seconds left. Obviously, a game-changing call.

Obviously it doesn't matter now, and there's no telling what would've happened. Horford ended up getting his free throws and didn't execute when he had the chance. But the Hawks are home, and the Celtics are on to the second round.