I'm having trouble missing any of these things
Religion- Didn't work right. Only two reasons to bother with it, micromanaging diplomacy and holy city cash cows. Which were a fix for the broken expansion penalty system. I'm sure they'll include it in expansions. Wonder how they'll do it.
Espionage- never thought they really got it to work right. Even in some of the better mods.
EndGame Win Movies- I don't miss the movies. I do miss the better endgame info screens. Since Civ I I've been enjoying the little replay map where it will show you conquering the world.
Wonder Movies- always skipped over them.
A Specific Civilization- 18 civs in Civ V, 18 in vanilla Civ IV. Endless mods.
City Specific Happiness Management- Oh god no. What a pain in the butt.
Tradeable Technologies- Meh.
Corporations- They got it to work OK in RoM. Didn't even have it in the vanilla Civ IV. It was BtS, right? It was broken in that expansion.
Unlimited Strategic Resources- Nope, I'm liking this better.
Civilization Starting Techs- couldn't care less
Bottom Right Scoreboard- I like the new UI much, much better. Even better than the improved UI in RoM. There are a few tweaks I would make. But I sure don't miss the old one.
A Civ4 Mod you used- RoM, obviously. Zappara's working on it.
The Music- to be honest, I don't like either. Sounds like elevator music. There are a few tracks in a few Civ V civs I've heard that I like, but nothing to write home about. Where's the Herbie Hancock from Civ II? They should hire the guys who make the music for Katamari Damacy.
The Diplomacy Overview Screens- I prefer the less quantitative approach. The leaders themselves look much better.
Global View- thought it was a novelty.
Civ4 Style City Micromanagement- Nope.
Needing to build Roads to Resources- it was tedious. Getting rid of road spam is one of the great unsung improvements in Civ V.
Square Tiles- Hex > win
The Civ4BTS AI- Alright, here's what everybody's whining about. I'm not seeing it. Sure, it's not brilliant, but neither was Civ IV's. Civ IV AI on offense? SoD. Civ IV on defense? Throw everything available at the stack of doom on the second turn, if successful then churn out units in every city, if unsuccessful watch every city fall.
Post-Game Line Graphs/Summary- this I miss.
Post-Game/Hall-Of-Fame Map Replay- this I miss.
Stackable Units- Don't miss it a bit. If I did, I'd use the stackable unit mod.
The Research Tree Layout- There are only slightly less techs available in vanilla versions. Not a lot to miss.
Permanent Alliances- is that gone? Didn't notice. I guess I don't miss it that much.
Leonard Nimoy- I like the new guy better. Like I said elsewhere, he actually seems interested in reading the lines. Nimoy sounded like he wanted to get out of the studio ASAP to grab some lunch.
So there you go. The only thing I really miss is the endgame. And that's not really a big deal.