This post will contain all my ideas and feedback I got from people playing the game.

Mechanics:

Human leveling up system: When starting from level 1, you'll find that the movement speed is really slow, I've seen many people complaining about it and quitting because of this. This also causes a problem when it comes to selecting perks (as what happened with cod zombies with the obligatory "crutch perks" like juggernog or speed-cola). Because your movement speed is so slow, you are left very vulnerable and you have no choice but to use all the points you first get on movement speed.
How to solve it: Make the starting movement speed a little less slow, so upgrading it isn't obligatory, but an upgrade.

Zombie leveling up system: The upgrades for zombie mode are a bit lacking.
How to solve it: Give the zombie more upgrades, go crazy, maybe even an ability to summon a circle of zombies around you that could be used to ambush and as a shield (of course this should be restricted use and only available by filling up a meter).

Sliding: it's always used as an escape method, the jumping across gaps mechanic that was introduced in the tutorial goes unused.
How to solve it: Implement something in the level design that makes use of this mechanic.


Tutorial:

The tutorial is almost invisible, I didn't know there was one until I saw there was an achievement for completing it. It is also flawed in the sense that it teaches you stuff via speech, which is in english, leaving part of the people with no clue what to do.
How to solve it: Make a text pop up when you first boot up the game informing the player that a tutorial exists and to try it if they are new (something like tf2's messages when you load up the game. Also, add a more "multi language" friendly approach to the tutorial by adding subtitles or by changing it to something more intuitive.


Story mode:

Maybe not a suggestion, but I've spoken to many people and they say they want to see what a story map would be, maybe upload concept art, screenshots or something that can calm the urges (even if it's very crude drawings or whatever).


Objective mode:

Quests: there's almost no quests available to complete. The one on termoil is broken, as sometimes you can complete it by killing walkers alone. Also, you have to get out of your way to find runners to complete said quest as they don't always spawn and are hard to find.
How to solve it: Make runners spawn with the other zombies on the main street. Fix the killing requirement detection, as I can kill one bandit and it'll count as if I killed 12 bandits and a runner (no joking, altough it is very random how it works). Finally, add more quests.

Mecklenburg: Too many zombies spawn inside the apartments.Getting the key to the gun shop is very hard, as the room immediatly fills to the brim with zombies in the blink of an eye.
How to solve it: Not too many zombies spawning inside the apartment. Nerf the key room zombies spawn.


Arena mode:

Someone mentioned adding an easy mode, but people seem to enjoy the gamemode very much. Maybe add more bosses that aren't Fred to add variety.


Player vs player gamemodes:

People don't seem to find much interest in playing these gamemodes as there are no rewards nor incentives to play them (not even xp).
How to solve it: Add achievements connected to the gamemodes (like "win x amount of games" or "Get to first place x amount of times"). Also, a separate leaderboard would get people more interested as there is a competitive incentive. There's also a demand for more maps.


Encouraging workshop content creation:

The content most seen in the workshop is weapon skins, especially "paintjobs". Why are they there? Is it maybe because people want to customize the looks of their weapons?
Now listen, I'm not saying to add official skins, but customizing your thirperson model is not as visually apealing as holding a colorful gun that you (the player) can see in first person.

Starting contests like skin making contest or map making contest could be a fun thing to do as a community and this will encourage the creation of workshop content. Mybe the rewards can be whitelisting weapon skins and having them as an equipable unlockable item that you can show to your friends and laugh at them peasants, or whitelisting the resulting maps for a short period of time and have a server let you play these maps and gain exp.


Weapons:

The last thing I'm gonna talk about is the mp5... I love having my eardrums pierced as much as the next guy... but please, I shouldn't need to dig into the files as to not get my ears pierced. Please fix volvo

Please don't take this the wrong way, it's just a list of stuff that can improve the game significally. Also, obligatory sorry for bad english xd