I find my games are hilarious enough without punishing multi-attackers and that just comes down to good description and making failure fun (for the players and DM if not the PCs and monsters). I have never seen any net upside to a formal system for critical failures.
The difference between a regular hit and a critical hit is roughly the difference between attacking normally and attacking with advantage. You could cause a critical fumble to grant advantage on the next attack made against that character (before the end of their next turn).I see no problem with a critical failure system in theory, but the implementation is hard. I would only use one as a balance to a critical success system, so to use 5E, it would only be a critical miss. The penalty should be about the equivalent to the benefit of a critical hit, so that creatures with multiple attacks aren't punished (just balanced). I would think the best method would be to grant the creature you attacked a critical hit if their next attack hits you (before your next turn). Still wonky, because ranged characters are hurt a lot less by this.
Some of the players in my game have expressed interest in having critical failures in the game. I will admit it is fun when the enemy rolls a natural one and things go hilariously bad for them, but the fact is that critical failures are far more devastating to player characters than to monsters.
It's also worse for characters with multiple attacks, like two weapon fighters and monks. The more you roll, the greater the chance that you will fumble. This also means that as you go up in level that your chance of a critical failure goes up. At 1st level you may only have one chance to fail, but at 11th level you have tripled your chance to fail. That doesn't make sense to me. Why would you critically fail more often when you get better?
So does anyone have a good system for critical failures that add some fun to the game, but doesn't punish players for making more attacks?
Mine is simple.
If you roll a natural 1 you provoke an attack of opportunity from the target of your attack.
I also have weapon damage rules, and on a natural 1 you have to make a weapon damage check if you're using a bow or crossbow.
The best fumble rule I've ever come across is just asking the PC who made the fumble to describe what happens. Those who enjoy auto-crit sneak attacking their own heads into four pieces will love it, and people who don't like added penalties for fumbles can make up a short flourish about they slipped on an invisible turtle and missed, but regained their footing.