With time running out in the 2nd half and the home team down by a goal, a corner kick is taken by the home team and the ball bounces off of a player and then a home team player heads it into the goal. The CR signals the goal scored and then blows a long whistle signaling the end of the game.

The home team players celebrate and walks off the field and the visiting players also walk off the field. As the teams get ready to exchange post-game handshake, refs approach both coaches and reverses the last goal as a ‘no goal’ citing an offside violation against a home team scorer and declares the visiting team as winner by a goal.

Can the refs reverse call(s) or non-call(s) made during the game after officially ending the game? If so, then is there a time limit or restriction on what type of calls or non-calls can be reversed?

USSF answer (October 4, 2010):
Law 5 (The Referee) tells us:

Decisions of the Referee
The decisions of the referee regarding facts connected with play, including whether or not a goal is scored and the result of the match, are final.
The referee may only change a decision on realizing that it is incorrect or, at his discretion, on the advice of an assistant referee or the fourth official, provided that he has not restarted play or TERMINATED THE MATCH. [Emphasis added.]

Since the referee had terminated the match, the goal decision has to stand and the decision to change it was in error (as well as protestable, because the referee “set aside a Law of the Game”). After including full details in the match report and submitting it to the appropriate authorities, all that remains is for the referee to either learn from this or turn in his badge.