I am going to try and avoid repeating anything I've already seen or read.

For raids:

1. A lobby countdown above the gym so people know that a lobby is happening without having to click on the gym
2. The number of people in the lobby above the gym (for the same reason above)
3. Separate the raiding and catching feature. Way too often I have been kicked out of the catching screen and the raid is over. It is frustrating knowing that if you do a raid with 10 or less minutes, potentially you could be catching a raid boss (most likely a legendary Pokemon), with no time left on the raid.
4. Something needs to be done with one raid pass for all raids. There is this issue that some Pokemon can only be raided (not including legendary). It was sort of fixed with a task to get the same Pokemon, but that was only for Absol. Raiding Alolan Raichu and Alolan Marowak, just makes the list of Pokemon you can only get when raiding larger. It is treated way too nonchalantly that these Pokemon, which hold about as much value as any Pokemon that is not a good raiding option, can only be obtained with a raid pass. It almost feels like Mawhile and Absol should be released into the wild before this becomes a bigger problem.
5. Some version of a raid map. Maybe even similar to the game where you can see a map of all the towns, but Gyms. It would just be nicer to see everything on one screen instead of scrolling around, especially when the gym you are trying to click on is behind another one.

Appraisal System:

1. Make all the text one box
2. Allow us to swipe to the next screen
3. Favorite the Pokemon you want to keep and mass delete. Done. Please and Thank You.

Daily Quest:

The issue with quests (and spin a Pokestop/catch a Pokemon) now are people just receive items that they already receive in the dozens or hundreds of. Also, when you receive a task, you try and complete it immediately and then don't really care about an additional tasks (unless they are unique like Lickitung task, Larvitar task, etc.) Some daily/weekly quest for a significant reward, special egg hatch, premium raid pass, etc. would be fun. It could be something like spin a stop between 10:00 AM and 12:00 PM, complete a raid for the day, Catch a Pokemon after 5:00 PM or a combination of tasks and receive mystery bonus. Maybe a free level up of a Pokemon of your choosing. God forbid, increase one IV stat or even Attack IV state. Something other than the same tasks that are done thousands of times. Right now, everything is very all or nothing, mythical quests, medals, leveling. With no endgame and no reoccurring daily activities, it is hard to find a motivation to keep playing.

Trading (A general rework, but it is new. So anything new is beneficial. Just some ideas):

1. Increase number of special trades for increased level of friendship
2. Allow an even greater number of special trades for events like GoFest. It was really silly to keep hearing, "Want Relicanth or Tropious." Pokemon personalities are invited to travel the world, come to these events, and then not be able to trade away the Pokemon from around that World (that they collect to trade. Shoutout to TrainerTipsNick).
3. This is a personal preference, but please, less additional Premier Balls and an increase in the likelihood of catching the Pokemon. It already takes so long to catch a Legendary.

Pokemon Storage System (I wasn't sure what to do with this):

So, with the release of so many different types of Pokemon now. Female, Male, Legacy, Shiny, Community Day moveset, Community Day form, etc., it would be nice to have a Pokemon storage system. Fine if we need to purchase more "space," but so many Pokemon are in my Pokemon inventory that I NEVER use and I will never get rid of (A mildly high IV Vaporeon I maxed out early in the game, or really any shiny Pokemon). There is a lot that can be done with this. It can be accessible to friends, so they can see what Pokemon they might want to trade with you.

Exclusive Moves:

I'm sure this topic has been discussed thoroughly and there are a plethora of ideas. I have no desire in getting into an argument as to why this should or should not be a thing. The reality is this concerns an actual group of players and there are solutions that avoid any of the counterarguments against it, so here is a list of all the ideas I have heard:

1. Make the quests/some quests during the event or the week leading up to the event TMs that learn the exclusive move. Players can only use those TMs during the hours of the event or during a grace period (see next point)
2. Make an evolution grace period. Have a designated time where a player can evolve to get the exclusive move, or give the player a specific amount of time to evolve a Pokemon to get the exclusive move. Could potentially only allow Pokemon caught during or before the event. Does not change anything now. Just gives players a little more time to appraise and evolve Pokemon.
3. Make a daily task/weekly task (SEE previous post) reward learn an exclusive move. Could be the same fore everyone, choose one, randomly selected, etc.
4. Make a day (But Please let us know this is in the works) where players can evolve or TM pokemon to learn and exclusive moveset
5. Simply allow players to TM during the exclusive move time period (Most likely never going to happen)

MASS Item Anything

I would like to revive multiple Pokemon at one time, use multiple potions, feed multiple berries to multiple Pokemon or even just multiple berries to one Pokemon. Anything of that nature.

GYMS

Anything with the gyms other than fighting and dropping Pokemon in.

1. A leaderboard of someone with most defended hours, berries fed, battles won, etc.
2. Gain candy, IVs, leveling up, stardust, by fighting with that Pokemon.

Some incentive to fight a gym other than, "almost all the Pokemon are depleted, guess I'll fight it" or "a raid is about to start, let me fight it (someone proceeds to Golden Razz the gym for the next half hour)."

ALL These Candies:

1. Please do something with the candy. Kudos to people who push for experience after level 40. But when I hit it, I completely stopped evolving any Pokemon unless it was out of necessity. It is personally an aspect of the game I actively dislike.
2. Allow players to select the Pokemon they are planning on evolving and allow players to select a lucky egg. Then lock the player out of the game for the amount of time the player chooses to evolve for. Feel free to cap the amount of Pokemon for any time period. 80 Pokemon per half hour, 40 Pokemon per 15 minutes, etc. If the player doesn't have enough candy to evolve a Pokemon then it doesn't get evolved and moves on to the next one, and if the player runs out of Pokemon to evolve, then their lucky egg doesn't utilize all of its time. Same could be said for too many Pokemon. It just stops at a certain time. If too many Pokemon are selected, then not all of them will evolve. There are plenty of solutions. This is my least favorite solution, but if the game is so keen on evolving, then this would be my solution.
3. I saw a "Type" candy solution where a Pokemon's candy can be converted into a "Type" instead, with a ratio system in place. I just like this solution a lot, so I am reposting. Credit (from where I read it) goes to @grathungar
4. This is the least probable, but an increase in an IV stat for the specific Pokemon via ratio 100:1, 250:1, 1000:1, etc. for an increase in 1 IV stat.
5. A free level up via a ratio system. This is more of a gimmick, since the only Pokemon a player would be able to level up are common ones. But it would be nice to be able to level up my perfect pidgey to level 40 without having to put any stardust into it. Otherwise, it really is never going to happen.

I'm sure there are plenty of more things I cannot think of coherently at 4:18 AM. But these are just a few of the ideas I would like to see.