chipperLike the NFL: A challenge system! With limits - let's say each manager gets two.
Not like the NFL: Don't put the head umpire in a little booth behind a curtain.
Instead, like the NHL: The umpire calls a video review headquarters, where a special unit handles the review. Don't make the umpires watch screens - take it out of the ballpark entirely.
Also like the NHL, the general rule is: If not conclusive, the ruling on the field stands.
Also, the umpires should have the power to invoke a review if there are differing opinions among them.
Make a list of what's reviewable and what's not. Safe or out at bases absolutely must be included, as fair / foul will probably be, and home run / not already is.
People are saying it would make baseball games even longer, and while that is nominally true, I sincerely doubt you would see this system abused - it most likely won't even be used every game. Managers won't issue pointless challenges - they probably won't issue any unless a team employee watching the broadcast calls down and lets him know about something the umpires may have gotten wrong.
Now, what happens in cases where play continued / would have continued after the disputed call? This could get messy, but a careful set of rules could take care of most of the permutations. We already have a "ground rule double," where if a ball bounces into the stands off the field, it counts for two bases. Similarly, things could be judged as "that should have been a out / single / double / triple," whatever.
It won't be perfect, and there will still be mistakes. In fact, as it is in the NHL and any sports league, not every game is equally televised - or televised at all! For instance, the net cam in the NHL only comes out in certain games, IIRC. But more often than not, the right calls will be made.