I think everyone id getting far too carried away with a series of nightmare scenarios where play is stopped while someone looks at a screen to see if there was a foul 10 minutes before. That is NOT what I would use TV monitoring for.
In the same way as they do for Rugby (both codes) the video ref would only be used when the ref called for him - which would only be when there was doubt over the validity of a goal or where there were claims that a goal had been scored but not given.
In these circumstances play would already have been stopped (either for a goal or a kick) and it wouldn't take long for the decision to be made. In the case of the Henry handball goal they hadn't even kicked-off when TV showed the handball. Even in the case of the ball crossing the line but being cleared and play continuing (as in the Spurs 'goal' v Man U) it would only be seconds before the ref was informed and blew for the goal.
Every second of every game is different. I dont think these are nightmare scenarios but things that are very likely to happen in games. You need to have some real hard and fast rules regarding when it can be used. Just saying when the ref needs it and in special cases only is way too ambiguous.
Any replay takes at least 10 seconds to come up on the screen, so much can happen in 10 seconds.