1. Advantage (and Disadvantage)
I remember the horror of a Pathfinder/3.5 combat where one gamer got lost tracking roughly 9 modifiers active on his character. If you were to get into "net" gains even without numbers, you can run into this, especially with higher level play. You could replace it with pure DM discretion of a range of plus or minus 1 to 4 based on how the DM sees that exact scenario, but then we run into consistency ("well last time I swung from the chandelier you gave me +2...")
I personally don't like the idea of 1 form of Advantage cancelling out 10, or even 3, sources of Disadvantage and if I were to tinker anything, it's this, solved by pure DM discretion to not allow it.
2. CRITICAL HITS (and Ability Checks/ Saves)
Easy to house rule if you need Nat 20 to hit, you can't crit. Makes sense though instinct says rarely will this come up.
Critical confirmation does NOT work with Bounded Accuracy. WAAAY too easy to confirm. Same for critical fumbles. The math doesn't work because the system was designed for ACs that kept going. Played this way for 3-4 sessions, bad.
Skill criticals, should a natural 20 always succeed? I'd have a 1 in 20 chance of doing some pretty absurd crazy things and/or knowing things (DC 30 checks) that are so obscure that only 1-2 people on the planet might know it. I like the idea that some doors are simply too strong and you're never going to break them down with your 7 strength. I'm also great with 1s not being auto-fail on skills, and the optional rule if your ability score is 5 or more than the DC, you auto succeed.
Critical hits are a thrill factor associated with gamer stories about the time they rolled that Nat 20 in the big fight... I'd keep em for that.
I tried using the Pathfinder Critical Hit deck of cards but sometimes the effects just didn't apply, and then I'd have to house-rule something because a crit should always do something. I came full circle to the idea that double dice is the simplest and fastest way to play it. I can't think of a good way to improve that doesn't slow the game down to check a chart.
Pure brainstorm that if you get 11+ over what you needed to hit, it's a crit? It could get nasty with multi-attack foes versus low AC foes.
3. FUMBLES (and Ability Checks/ Saves)
So long as there's no negative other than "you miss" for a natural 1, it's not a big deal. We can't penalize higher-level fighters and the math on confirmation doesn't work like it did in 3E.
Pure brainstorm that if you get 11+ less than what you needed to hit, it's a fumble with a consequence, max 1 per turn? My Pathfinder critical fumble deck might come in handy, spells included, and if you get lucky and the effect is impossible, great. Take a deep breath and count yourself lucky.
This rewards the math for higher AC inducing greater chances for a fumble. I previously capped the # of fumbles you could have because I didn't want to over-penalize beings with multiple attacks.