While I understand the appeal from a team's and fan's perspective, I just don't see how such a system is feasible in real life.
Let's start with reiterating a point that too many people forget - almost all penalties committed in an NHL game, both called and uncalled, exist somewhere in the gray area between absolutely and ridiculously illegal and legal hockey play. There are very, very few penalties that are called precisely along objective criteria, the two most clear being Delay of Game - Puck Over Glass and high-sticking.
That isn't to say some plays aren't clearly illegal. When you see the highest-end hooks, boardings, illegal checks to the head and whatnot, it's obvious those against the rules. But the measurable tipping point for when a normal hockey play becomes illegal is very gray. And that's because almost all of the illegal things in hockey stem from a good play gone too far. It's legal to try and use your leverage to pin down someone's stick with your own, but it's illegal to break it or knock it out of his hands. It's legal establish your own body position in an area of the ice, but it's illegal to knowingly step into another player's path to pick them off. It is legal to throw a solid hip check, but it's illegal to put your body so low that it takes out your opponent's knees.
Given that, and given the incredible speed of the game at the NHL level, most calls, good, bad or ugly, are going to incur someone's wrath. And that's before you account for the fact that referees are human and therefore make mistakes.
The best comparison I can come up with is that a good referee is like a great goalie, with a save/good call percentage clearly above the 90 percent mark. Most of the misses will be defensible as well - perhaps the ref was screened by three players or it was a terrible combination of sightlines and luck or there even might have been an embellishment along the way. And sometimes soft calls just happen, like soft goals will sneak through even the best goalies. As long as those completely indefensible calls don't happen often, you just have to live with them.
And going back to replay for a moment, you have to remember that there is no clear black and white criteria on nearly every call. If they called the game by the letter of the law all the time, about 50 percent of the players would spend the entire game in the box. Take hooking for instance.
A minor penalty shall be imposed on a player or goalkeeper who impedes the progress of an opponent by "hooking" with his stick. A minor penalty for hooking shall be assessed to any player who uses the shaft of the stick above the upper hand to hold or hook an opponent.
That happens, per the strictest interpretation, at least once a shift in an NHL game, from fairly legal stick-checks with minimal hand contact to "herding" a player with an extended stick in your own zone to tiny tugs on the hip to a full-out can opener. While I understand the appeal for a clear dividing line between cheating and not, it's simply not possible with the way the rule is conceived unless you want 3-on-3 all the time.
A referee, then, is as much an artist as he is a judge. He has to understand which penalties have an impact on the flow of a game and which don't. He has to know when it might be time to hand out a lower-end call because things are getting completely out of hand. He has to know which players are combustible and understand how to head that off so it doesn't boil over into violence. And he has to do all this while tracking the play and watching everyone through continuously changing traffic patterns.
It's an impossible task from the get-go, and introducing a limited amount of coach's challenges a game will do nothing to address this. The vast majority of calls wouldn't be able to be changed because there would be no clear and conclusive video evidence to overturn the call, particularly given the actual wording of the rules. Trust me, I can find some sort of minor hook or other infraction on 95 or more percent of the hooking calls out there.
The general argument most fans/play-by-play crews/coaches make when discussing a bad call is that the penalty made didn't meet the standard of call that had already been applied in a game, but there is nothing about a video replay that can conclusively and objectively prove that. You can only judge by the standard of the rule as written, and they are so broadly drawn that you can find a violation in nearly everything.
Are there divers that might be caught using a review system? Absolutely. But I would argue a more effective way to control this would be regular post-game review for embellishment by players and the establishment of a tiered disciplinary system to eliminate the problem before it begins. The more you can make the risk-reward equation of embellishment tilt toward risk, the less likely players are to try it.
Finally, none of that addresses the problem of missed calls, which I would argue are as impactful or more than poorly made ones. Given the flowing nature of a hockey game, there is no natural area in which to insert a review period for missed calls (and again, you can find something that could technically be whistled on almost every play). There's already far too much confusion about what happens when a goal is missed in the run of play (time reset, subsequent goals wiped off, penalties stand except for those of a "delayed call" nature against the team that got scored on). Adding another layer to that would just lead to additional chaos.
What do other leagues do about this problem? Not much more, if at all, than the NHL currently does. Of the three major North American professional leagues with penalties (this excludes baseball with its lack of something parallel to a foul), illegal action is reviewable in two of them, but only in very specific circumstances.
The NBA allows video review for "clear path to the basket" fouls, only after they have been called, to determine if the clear path to the basket criteria was met. This is easy to see on a video replay when you can conclusively determine if there are opponents between the fouled player and the hoop, where the foul occurred on the floor and where the play started. Last offseason, the owners voted to expand replay to include extra review of all flagrant foul calls (as opposed to just flagrant 2 fouls) and late game goaltending/restricted area calls (again, calls with fairly objective criteria - in or out of the area, upward or downward path of the ball). And even that one has come with some controversy.
You could argue the NHL might allow reviews of major or match penalties to be parallel to the NBA's reviews of flagrant fouls, and there is some merit to this. Again, though, I think the vast majority of these would be allowed to stand because of the subjective nature of the rules involved. It would be most effective with the illegal check to the head rule but would rely on the semantics of "targeted," "principal point of contact," "vulnerable position" and "immediately prior to" far too much for my liking. The other calls typically ending in majors - boarding, charging, checking from behind, etc. - are some of the most subjective on the books with almost no black and white criteria to apply to a video review.
The NFL allows precisely two penalties to be challenged via video review - 12 men on the field and illegal forward pass. Again, you go back to the question of objective criteria, and these are easy to understand. Procedural plays with objective criteria - forward/backward passes, fumbles, touching of a kick and so forth, are also reviewable.
The leagues do not and almost certainly never will allow challenges of subjective calls like holding, illegal screens, pass interference and hand checks. The logistics are just nightmarish.
What the NBA does do better than the NHL is use post-game measures to punish flopping and disclose the judgment errors on the most egregious of blown calls. While this certainly is not a comprehensive list of all the calls that could have gone the other way in every game, it does give the league a little more credibility in the eyes of the public for owning up to mistakes. For the blown calls of the greatest magnitude in the NHL, I wouldn't mind something like this. I assume the NHL does not do something like this because it could never make everyone happy with the calls the select (or more importantly, don't select) to detail, and I also understand that perspective as well.
On the embellishment side, I would argue the use of off-ice/off-court replay to regularly punish diving/embellishment is probably the biggest step any league could take to upgrade the quality of officiating. So much of officiating happens on split-second decisions where the result of the play is as important as the illegal action itself that embellishment has a huge effect on how a given play is called. The more you eliminate the antics of players like Dustin Brown, the better all calls will get.
But fans will always be unhappy over borderline calls, no matter how many times you explain why it might have happened or might have been missed. For instance, you can explain goalie interference until you're blue in the face or directly link to the handy little chart in the back of the NHL rulebook and they still will howl about how unfair a call was. That's the nature of fans, and I can cheerfully admit I have a hard time legitimately evaluating calls for and against the Stars for the same reason.
So what, then, is the solution to bad calls, at least from a fan frustration perspective? There really is none. This is a game played by humans, designed by humans and officiated by humans. Bad calls are simply going to happen. The real key is not to minimize or vilify them when they do, but to identify ways that call could be reasonably prevented/made in the future. Unfortunately for hockey, that does not lend itself to an instant replay review system but to more complicated issues like eliminating diving and defining clearer standards for calls that apply from your fourth-line grinders to your 10-time all-stars. Neither is a quick fix, and neither will lead to perfect officiating.
If you spend way too much emotional energy getting frustrated by bad calls, the best advice I can give you is this: Educate yourself on the rules and their general unwritten standards so you don't rely on announcers, who vary in quality from absolutely objective and knowledgeable to complete homers. Look for cues that might lead to calls, such as reaching with a stick or hitting someone hard in the 2-6 foot zone from the boards. And take a deep breath like you do after your favorite team's goalie gives up a soft one. Bad calls happen to good people, and until the hockey world decides to completely rewrite its rulebook, that's just going to be part of your life as an hockey fan.