There's no denying that the umpiring has been bad this postseason. The "human element" defense of bad calls is complete BS; men that aren't playing be able to affect the outcome of a baseball game by being bad at their jobs. Something needs to be done. But what?
A challenge system like football wouldn't work in baseball. Football coaches are constantly in contact with other coaches that can view replays and tell them if a play merits challenging, and most coaches still miss on more than half their challenges. Setting up a similar system in baseball, where managers generally don't have staff in a box reviewing plays, wouldn't work.
What I think would work is a system more like hockey. Expand each umpiring crew by one with the extra member being an unseen man in the press box or in the van with the TV crew that has access to all of the cameras that make up the TV feed and the replays. Keep him in constant communication with the home plate ump or crew chief via a Bluetooth headset, and use him like a fifth (or seventh, in the playoffs) ump. Team appeals a runner leaving early at third? Ask the guy in the van. It can work the other way, too. The guy in the van sees that two runners were tagged out and the ump only called one? He can tell the ump with the headset what happened. Keep the same rules as football; the guy in the van has to signal there's a problem before the next pitch or play moves on. If this guy is working in between plays, there won't be nearly as much downtime as people expect.
What's the worst that could happen here? It does end up being time intensive and it has to be ditched? At least we'd working towards a solution instead of insisting that a broken model doesn't need fixed.