Shortly after the release of the main game the developers release the first big Patch 1.0.1.

It fixes problems with Controllers, Resolutions and a lot of other things.
Sadly it doesn't fix my problem with my wireless Xbox 360-Controller not being detected.
I'm thankful for every hint!

Here is the full announcement from Steam:

Improvements :
- Updates the controller plugin
- Adds a "Restore" field on the keyboard remapping screen
- Adds a move list screen (gamepad and english only) accessible by pressing Right on the remapping screen
- Adds the ability to remap inputs as arrows
- Removes the obligation of playing as Player 1
- Adds ability to hit jumping dogs with single punches
- Tweaks difficulty on some story levels and arenas

Fixes :
- Fixes a crash when plugging/unplugging a gamepad on the menu
- Fixes "Don't play with knifes" achievement
- Fixes the way of unlocking "Broforce" and "Peace" achievements
- Fixes a NPC animation when doing a 2nd fatality when the 1st was not completed
- Fixes a player freeze when the injection is done while being flatten by the train
- Fixes a memory leak on the menu
- Fixes a non recognition of inputs on the menu if player hits Escape when a bot was added
- Fixes the button display refresh on the menu when remapping keys
- Fixes the player animation stuck on self injection
- Fixes Petukhi being stuck if the cinematic is launched while he is dead
- Fixes the ability to go forward if the Petukhi is dead
- Fixes a way to go trough the closed door next to Fixions concert
- Fixes the rail sound being looped after boss death
- Fixes riot girls behaviour before the first cop cinematic
- Fixes player AI behaviour in the first crisis of level 8
- Fixes music not being played after loading last checkpoint
- Fixes music pitch staying high when berserk stops
- Fixes menu display on a 21:9 screen resolution
- Changes 2160p resolution which was set as 2610 height

Known issues, need log files and more time to be fixed :
- Game crashes randomly when playing ('Attempt to access invalid address.')
- Game crashes on startup ('Fallback handler could not load library [...] xinput1_4.dll')
- Game freezes on "Press Start" loading screen (we need a log file from someone who has this problem)

About custom controllers not being recognized, please refer to this list if your gamepad is in : http://guavaman.com/projects/rewired/docs/SupportedControllers.html