5th dnd – Are these rules for critical hits and critical failures just right?

My group uses Critical Hits Revisited to improve critical effects. It seems like it sounds a lot like what you're asking for (thought limited to combat, not capacity checks / saves) because once the player rolls a 20, he rolls a second d20 to determine the nature of the criticism. It would be simple to do the opposite with failures.

we really like the way it allows a "gravity curve" and not a simple procedure of "you double the damage." For example, if a player strikes with reducing damage, this can result in a background effect (in addition to any additional damage). But if a player / creature does particularly well, the target can accumulate a variety of injuries that have both narrative and mechanical ramifications.

In the case where a player throws a pair of 20 with a sharp weapon, the result is a direct decapitation, the hands (heads?). That's actually produced with a shot my group a few weeks ago. A new player eventually beheaded Rivalen Tanthul in a meeting.

One thing that makes it really nice is that it creates a kind of mini-game from the criticism / failure. Once the first die is thrown, you know that something is going to be good or bad, but you do not know. How good or bad or the nature of the effect.

Then you have the narrative implications. Things like persistent scars, a box, eyes for missing eyes, not to mention the effects on mental health. We found that a system like this adds a lot to the game.