I wanted to correct something, in Baseball, they do have reviews for some things, but they don't review strikes/balls because they recognize that human error is part of the game. To me, Football is the same way. Its not an exact science, they call it the beautiful game, not the precise game. Sure, I feel robbed after last night but I think this thread very much demonstrates the logistical complications involved with adding a review process.
For me, the "three challenges" idea fundamentally alters the way the game is played. I think teams would burn them to waste time when they want to run out the clock, and it gives managers another thing to worry about in late stages of games. It also could be an effective way to stop an opposing teams counterattack (keeper saves on the line and the other team is breaking up the field, might as well use a challenge).
I would be okay with automated goalline technology. It would have to be nearly 100% accurate though, as I would hate for goals not to be given for malfunctions. Even a fourth official review of a camera would be fine with me, because that should not take more than 10 seconds for a layperson, let alone a competent official.
I would not be okay with reviews of offsides calls, if we had this, linesmen would tend towards not flagging close calls (knowing that if the result is a goal, it'll be reviewed). This both changes a linesman's job, and it would lead to many more plays being allowed to carry out, only to be called back later. I think this would disrupt the flow of games, with many goals being scored, only to be called back.
Would you really feel much better about a goal disallowed because a millimeter of a striker's boot was passed the defender at the precise second a ball was kicked, just because it is consistent with the letter of the laws of the game? To me thats just as bad is if its disallowed when the players are about even, with no review.
The best solution to offsides problems for me, is to instruct linesman to call offsides the way the rules specifies PRESENTLY, which is to give the attacking player the benefit of the doubt if the two are about level. It will no doubt take some adjustment since so many teams play a tight offsides trap, but I think it would get rid of a lot of the inconsistency.