Alright, here are my ideas, for anyone who cares. I’ll be editing this post to add to it, so these changes aren’t in any particular order, just what came to mind first.
1. Differences between male and female characters: Obviously there should be differences between genders when it comes to story and NPCs should react differently to you depending on your gender. For example, if you play a female, you shouldn't be able to join a misogynistic band of raiders/slavers that cosplay as Romans. But as far as gameplay goes, there should be some actual, tangible advantages and disadvantages that males have over females, and vice versa, much like those that exist in real life. It doesn't have to be balanced either. I'm okay with the game being harder if you're a woman, or at least force you into different playstyles, kind of like in real life.
I think female characters should have a -1 (maybe -2) modifier to all Strength checks, forcing you to put more points in Strength if you want a female character to be as strong as a male. Maybe women are more affected by drugs, or get some kind of bonus to Speech. Maybe women can kick more accurately than men (yes, that's a real thing).
2. Expanded Karma System: Most people think that Karma has outlived it's usefulness, and that the town reputation system is a better replacement for it. I'd have to agree, but I think a Karma system can still be used. Karma needs to be revamped to accurately portray the more gray areas of morality. I propose that instead of a sliding scale of good to evil, there should be a separate tracker for good karma and evil karma, like in Mass Effect. But the Mass Effect morality system isn't that good either, so let's expand this some more.
There should be three different "types" of Karma: Honorable, Pragmatic, and Psychotic. This way we can use Karma to track the various shades of moral ambiguity that exist. For example: having high Honorable karma but low Pragmatic and no Psychotic would mean your character is seen as a hero that never compromises in the face of evil, never kills if he doesn’t have to and rarely even accepts payment for his deeds. A character with high Pragmatic and Honorable and no Psychotic would be seen generally as a hero but one that is willing to get their hands dirty and perform immoral acts in the name of the greater good. A character with high Pragmatic but low Honorable and no Psychotic would be seen as someone who is purely self-interested, like a mercenary or thief. A character with high Pragmatic and Psychotic and low Honorable would be seen as cold-blooded and ruthless, but not the kind of person that just kills impulsively. A character with high Psychotic and low Honorable and Pragmatic would be seen as a bloodthirsty psychopath with no self-control.
Sure, it's needlessly convoluted and it would be better to just drop Karma entirely, but I thought I'd just throw this idea out there.
3. Drugs: Drugs were one of the most innovative things the originals did in my opinion. They were a nice way to have "potions" exist in a magicless modern/futuristic world. And they mimicked real world drugs by causing addiction and having withdrawal and coming down systems. I think this could be expanded on by allowing you to overdose on drugs as well. In fallout 2 you are limited to taking two of each kind of drug, after which the effects no longer stack. With overdosing, drug effects could continue to stack (but probably decreased benefit for each successive dose taken), balanced out by the fact that if you take too much it can lead to some serious negative effects, possibly even death. Mixing drugs could amplify your chance to OD as well. How much you can take before you OD would depend on your endurance.