Cricket, American Football, Rugby Union, Rugby League, and Tennis are just some of the sports which use technology to aid the officials. These sports do have a stop-start element to it and this is the main argument behind not adopting the technology in Football. It will create too many lengthy stoppages in play.
A typical scenario would be a debate over whether the ball has crossed the goal line or not? We have seen that it takes less than 10 seconds to get a replay up, 30 seconds for a decision to be made (less so in obvious cases) and less than 5 seconds to get the message back across to the match referee. This comes to a maximum of 45 seconds which is not an excessive cost since a typical goal celebration will last approximately the same amount of time.
There are other issues over how far you should take it, did the ball cross the line for a corner? Who did it come off last? Penalty decisions? Offside decisions? Or even if the ball crossed the line for a throw-in?
It would be an idea to just start with goal-line decisions and work from there. The success of this, which will breed efficiency, can lead the way for technology to be used over other decisions. With the stakes so high and the margins so small, can we continue to rely on human impulse?
The other side of the story, for some, is what would we talk about if all the decisions were correct? The idea that we need to debate about such matters is ridiculous. Even then, there will still be scope for debate as the final decision will be made by a human anyhow.
The final thought comes on where to stage the idea? The trial needs to take place on a large enough scale to matter but not so large that it can bring the game into disrepute. My suggestion would be the experimental Europa League. The Europa League has already trialled the idea of 5 referees in a recent Everton-AEK Athens game. The problem is that goal line decisions are quite rare and a true reflection cannot be seen in just one year. So perhaps a challenge system over offside decisions could also be tested.
The sporting world has moved on and has not suffered as a result, it has almost come to the point that a man can lose his job over these decisions and this is not something that we should play around with.

I think the big problem will be deciding where to stop with it – cricket has faced this dilemna, i.e. should LBW decisions be referred? Football (soccer) will be the same; what happens if a referee can refer a bad looking foul, to decide whether he should book a player? I cautiously welcome technology, but I think clear lines need to be drawn under a limited set of decisions that can be referred, including whether the ball crossed the line. If we end up with referrals for, e.g., every offside call, the game will become tedious.
I think they can take it as far as they want so long as it does not affect the tempo of the game.