[Sekto Springs]

I agree that Abe should be able to hang from ledges. That's a big one for me.
I hated having to do precision jumping, especially when crossing water via those circular platforms. You could argue that it made it more of a challenge, but I didn't feel challenged so much as irked. I think the front flip style jump is fine, as long as it has more control.

An improved drowning animation for Abe would be killer. Instead of just flailing around in the water and then fading out of existence. Have his lifeless body sink to the bottom, or disperse into birds. The latter would be a good throwback to the old games.

On that note, having enemies fizzle away like the original games would also be a nice touch. I've never been a fan of corpses just vanishing into thin air. If you're going to remove the bodies, at least do something interesting with it. Stranger's Wrath had the right idea with the "rotting away" effect.

Allow for inter-species interaction between characters. I hated that when Munch tried to address the mudokons, they would just laugh at him. Record some sensible dialogue of the muds showing distrust, or saying they only parlay with Abe, or outright dismissing Munch.

Possessed sligs should be able to actually interact with other sligs beyond insulting them, and maybe even allow possessed sligs to interact with mudokons. I remember one of the early ad campaigns for MO featured some footage of a possessed slig addressing a mudokon, and he promptly responded with "Hey Abe!". That would be interesting, but would probably call for some of the puzzles to be redesigned for it to be utilized in any significant way.