The biggest single change I have to make--or at least by far the most work to implement--is reworking the monster list so that it is geared towards a bounded accuracy paradigm.
You may ask (I know I did) what exactly is meant by bounded accuracy. Unless you've been following the development and launch of D&D 5e, you probably haven't heard the term. The concept is simple: flatten the power curve. Characters no longer have runaway growth in all stats, to-hit rolls, skills, etc. Characters may grow into being able to face new challenges, but they never completely grow out of being challenged by prior challenges. In D&D of editions past, the notion of 4th or 5th level characters--to say nothing of higher level characters than that--being challenged by even large groups of kobolds or goblins was ridiculous. Under a bounded accuracy paradigm, all characters, regardless of level, have to watch out for these challenges, at least in large numbers.
How does this work? Mostly by shifting the To Hit and Armor Class escalation as level goes up to one of hit points and damage. If characters have only very modest increases in To Hit and Armor Class scores as they increase in level, then goblins will always be potentially challenging if you run into enough of them, because they can always hit you. However, if your hit points and damage output go up, then goblins become minions (if they weren't already) and you can, at least, face larger numbers of them, because the ability of any one given goblin to wound you in any significant way is reduced. You hit and are hit more often, and do more damage with each hit you do. In this way, larger and more dangerous monsters are more dangerous because they also have higher hit points and can deal more damage per attack, not because their To Hit and Armor Class scores are necessarily really high (although for challenging opponents, that may well be true as well.)
By the same token, Skill checks and saving throws (both in m20 implemented by a check of your relevant Ability score + relevant skill bonus + d20 vs. a target Difficulty Class, or DC) don't really change too much as levels increase either. For a d20 Rogue at 1st level, a DC 15 Lock that he wants to pick is a standard difficulty lock. For a 10th or 15th level Rogue, a DC 15 Lock is childishly easy. This is verisimilitude breaking; under a bounded accuracy paradigm, a DC 15 Lock is always a standard DC lock. And while a higher level character might be expected to pick it more easily than a lower level character, it's never trivially easy, because DCs are more static as well.
So, how would this be implemented? In my standard m20 game, a character at first level has hit points equal to his STR score + 1d6 and gains an additional +1d6 at each level gained. On leveling, a character also gains a +1 to his skills and to his To Hit roll. He gains a bonus to his AC equal to his level divided by 2 (rounded down), or +1 every other level. He gains a +1 to an ability score every three levels. Fighters gain an additional +1 to To Hit and Damage at levels 5 and 10 (in addition to what they gained at 1st) and Experts gain a new Affinity every three levels. The maximum level supported by the system is 10th level, which forces a kind of bounded accuracy of sorts.
Under a new bounded accuracy paradigm, characters would not gain all of these bonuses each level. Instead, they would gain them according to the chart below. Fighters would continue to gain an additional +1 to Hit and Damage at 5th and 10th level (and also, now, at 15th and 20th.) The Expert affinities would slow down a bit; every four levels (there's only so many affinities after all), so in addition to the 2 he gains at 1st level, he would gain an additional one at levels 4, 8, 12, 16 and 20.
All characters gain an additional +1d6 hit dice per level (although they would no longer gain the additional +1d6 at first level.) Characters will gain a bonus to their To Hit according to the chart below. Characters will also get additional damage dice (not unlike a Rogue's Sneak Attack skill, although it would apply to any attack; melee, ranged or even magical) at certain levels, as indicated below.
Characters will also gain more than one attack as they progress; eventually being able to attack up to 4 times per round. However, GM's need to be advised that this doesn't mean that characters are moving across the battlefield like the Flash, at super speed, hitting tons of enemies all at once. Most of the time, these additional attacks can only be used against a single opponent, although occasionally a GM could rule that bunched characters can all be attacked in a single round, since they're standing around next to each other.
Characters also gain a bonus to their Skills, but no longer at every level--it follows the progression listed below. And characters gain additions to their ability scores. This is a little different than what was done in the past; characters get two points to spend. These can be spent on one ability score (to therefore bump the bonus up +1 reliably) or they may be split across two abilities. No ability score can be increased above 20 using these; if for some reason a character has a 20 in all three scores--first off, wow, that was some excellent stat rolling at character creation, and secondly; any ability score increases are now lost. You simply can't go above 20, full stop. Sorry.