Things I'm still thinking about: henchmen, retainers & followers. They were a big deal at some tables.
Was just thinking about the topic and found this thread. Loyalty is covered in Tomb of Annihilation and in the 5e Dungeon Master's Guide, but nowhere to the degree it is covered in the 1e AD&D DMG.
I was initially thinking of keeping the 5e system, but using all of the factors in 1e Loyalty to affect the numbers in 5e (translating the 1e percentage system to the x-to 20 5e system). Seems too-simple. I am definitely interested what others have to say on the matter.
What I long for most: the 1e AD&D Bard. The intricate Non-lethal and Weaponless Combat Procedures. The Construction and Siege system and how everything in the 1e AD&D economy logically fit.
What I like about 5e: Subclasses and Feats, especially how they integrate to the underlying Ability Score system. There is a ground truth in 5e that 1e could never muster. Well, except the economy funny enough. There is an ontologically-creative supersystem in 5e that makes a Tiefling Druid, an Aasimar Sorcerer, and a Drow Bard in reach -- approachable. There is an immediate, nodding affirmative response to the Gnome Paladin, the Dwarf Wizard, and the Halfling Warlock. It's elevated.
What I love about 5e: Combat is fast. I've been stuck in 1e AD&D combats that last hundreds of rounds. Funny again is the action economy in 5e. It creates a flow that moves things forward while keeping it interesting the whole time. If the dumb Evil Wizard keeps spamming an Abjurer Wizard with Fire Bolt, the Abjurer can counter-strike (Reaction) with Absorb Elements (reducing the fire damage, raising the hit points of the Abjurer's ward, and returning the fire damage along with a quarterstaff, dagger, dart, light crossbow, or sling -- unless of course the Evil Wizard uses Reaction for Shield!). There is an overall capability to preempt, disrupt, deny, degrade, and make short work of adversarial combat effects. A party generally knows when they are outclassed and they don't die figuring that out -- or, at the very-least, there are more outs.
What I like/love about 1e: That classic feeling -- something beyond just nostalgia. The feeling of adventure from the point of view of children riding their dirt bikes into unknown, uncharted territory. The Goonies Effect. There's a reason that Speilberg and D&D are making a comeback and it's not just nostalgia: it's the Great Unknown. 5e doesn't capture that and it never will -- it's just resold dreams.
Not to end this on a terrible note, I think that 5e can be improved in this way using the Crossroads model, not just by leveraging old rules. Maybe mine is a more-strategic and less-operational way of thinking, but here are my first thoughts -- sorry for the stream-of consciousness writing style.