[Dave Brost]

Not sure if this is the correct procedure, but this is I would have done. If in the judgement of the officials as a group, the inadvertant whistle did not stop any players from playing, I would allow the action that happened after that to count, get a judgement on what amount of time should have run off the clock, remove that time, and play on from there.
What probably should have been done was, the official with the inadvertant whistle should have blown the whistle again, suck it up to admit the wrong-doing, and give the ball to the team in possession at the time.