Admittedly the 2 decisions yesterday would have taken 30secs to sort out but there are loads of decisions which aren't that easy to decide on, and can even be argued either way after the game with different people seeing different viewpoints. Ultimately the decision will still be subject to human error and depends on whether the video footage shows the incident in a significant enough detail (this was actually bought up by some Super League coaches in Rugby League as an argument to discard the usage of video replays)
There would need to be clear boundaries for the types of incidents covered by replays and also a limit to the number of challenges
As for restarting, in all sports that replays are used in, there are clearly defined points at which replays can be used and at which play can continue:
Rugby - try or not (with penalty or scrum given if not)
Tennis - point won, lost or replayed
NFL - TD, penalty, yardage gained/lost
Cricket - In or out (batsman continues or is replaced)
For football, the decision to challenge an officials decision neccesarily might not occur on a break of play
In the case of the Mexico - Argentina game it would have been simple, either a goal or a free kick to Mexico for the offside
In the case of the England - Germany game it isn't as clear cut. This is due to the fact that Germany launched a counterattack and only just put the ball wide of the goal. It might also be possible to abuse the system, eg challenging a call just to prevent a side catching you out on the counterattack (say if England felt that a German had handled a ball in the buildup to either the German's 3rd or 4th goals). This would completely ruin the flow of a game and allow teams to effectively cheat by stopping teams breaking quickly
The only way of preventing this is to have some way of penalising a team for an incorrect challenge (eg in NFL they lose a time-out, tennis they lose one of their challenges), but then the act of challenging shouldn't occur too often in a football game