Yes, they need to figure this out. The only problem that I see with instant replays is how the match will be restarted if the ball wasn't in the goal. You can't just take the ball away from the attacking or defending team. You'd basically have to wait until there is some kind of break in the game like a foul. And what happens if the other team scores while this all is happening and it turns out the game shouldn't have been allowed to go on?
So basically they should just put a chip in the ball and make it work. It's the easiest/best solution.
Apparently there are a lot technological difficulties with having a chip and the like. It's possible but not always implementable. Also, it doesn't address the issue of offside goals.
As it pertains to a goal that wasn't registered in play, this sort of thing happens alot in hockey. Yes, after the play is dead they review the tape, if a goal was scored the clock goes back, and if a goal was scored after it, it is negated. If the contested play is called a no goal, all the play after is deemed legitimate.
In the World Cup however I see the referees walking around with microphones and earpieces on. The play can be stopped immediately if the ref is notified of by, as Nefilim says, a TMO, who should constantly be reviewing footage as the match is played. For example, a simple "stop play, goal scored at 14:50".