No idea how a Third Umpire can give wrong decision... if there was 1% element of doubt, as per rules, benefit of doubt goes to batsman.
Clearly a no ball bowled by Broad to Williamson and it was not considered so.
One of the CricInfo comments: Everyone else in the world including Broad thought it was a front foot no-ball except for Steve Davis, which really mattered!!!" It was generous, Manic, though I think third umpires are loath to give those.
With Williamson striking the ball superbly, this decision was super crucial. It might had New Zealand's game... if Steve Davis would had given the correct decision.
Now, just to cover it up, I hope Aussies win tomorrow and NZ qualify.