There is a fundamental lack of understanding of how soccer is officiated. I'll give a brief overview of how it's done.
The center ref is absolutely in charge of everything that happens. None of the other refs make any calls, which is why the linesmen are properly called "assistant referees" and the guy in charge of substitutions is is simply the "fourth official." The linesmen are responsible for signalling offsides and whether the ball has crossed out of the field of play (throw-ins, goals, goal kicks, and corner kicks). He may also signal a foul if he doesn't think the center ref sees it. The fourth official does the book-keeping - he tracks substitutions and time which needs to be added due to stoppages of play.
The center ref can overrule any of the indications of the assistant referees depending on his interpretation of the "Laws of the Game," because the most important words in the Laws are, "In the opinion of the referee..." All refs in the World Cup have been referees for many years and have passed rigorous auditing to achieve the status required to referee at the international level. Many of them have played at a high level prior to becoming nearly full-time professional referees. Thus, they have participated in hundreds or even thousands of games either as a player or ref before they ref a single international game. They ref many international games and receive good marks before they are even considered for the World Cup. Thus, their opinion is based on their interpretation of the Laws, their vast experience as player and ref, and the context of the game. Having played soccer at a high level and reffing at a much lower level, I can definitely say that context makes a big difference in whether or not a foul (or a dive) warrants a card, whether a foul is worthy of a penalty kick, and so on.
Putting another official in charge of reviewing replay footage would fundamentally change the Laws of the game from the ground up by giving the final to someone other than the center ref. FIFA was willing to implement an objective system to determine whether a shot was a goal, but the system did not meet the required level of accuracy in the practice tournament and they made the judgment call that it was too risky to use in the World Cup based on that outcome.
I have watched every game in the World Cup so far, and I absolutely agree that there have been plenty of blown calls. I don't think any of these calls have adversely affected the outcome of the tournament. The only call which probably changed the result of the game was the reversed goal in the US v Slovenia game, but in the end it made no difference in the tournament whatsoever. The two goals in question in yesterday's games were no doubt incorrect calls, but I do not think they had any impact on the ultimate result (other than helping me meet my fantasy cup score prediction ).
Offsides is by far the most difficult call in soccer. Not only does the linesman have to keep up with some of the fastest runners in the world, but he has to watch the ball, offensive, and defensive players all at the same time. It is also very frustrating as a player when the call is blown, whether you're on offense or defense. However, the offside rule will never fundamentally change because it gives the game extra dimensions of creativity for both the offense and defense. It would be great to get it right every time, but logistically, allowing replay review would always work in favor of the defense because if a false offside is called, the offense has already lost its advantage when the play is whistled dead; if a true offside is not called, then the defense will get the proper advantage in the form of a free kick.