Well, to add what is being said already:
there's many instances where a questionable decision (or, a proven wrong decision) eliminated teams from various competitions, there's a lot of money to be lost for a club when it misses out on a Champions League spot, for example, and careers can be wrecked by things like the Henry goal against Ireland.
So yeah, I fully support some fallback solution.
Goal line technology sounds like a good solution as it is fast and precise, and with the speed replays can be conjured up these days, other applications of a review are certainly viable.
When FIFA says it should be played the same at grass-roots level as it is played in the highest tiers, they're only making a convenient excuse against change.
And, for other possible game-changing moments like a questionable off-side or a penalty decision, why not implement something akin to the "challenge flag" used in American Football?
Basically, every coach gets one or two challenges per game to be used at any time so a decision can go to the video ref to determine the validity of the on-field decision. That wouldn't take longer the babble on the field either and would ensure that game-changing moments are based on a correct call.
On a side note:
I vote for a change in rules that says: a dive in the penalty box is an automatic red card. The punishment for a caught should be equal to the reward for not getting caught.