I just got the game the other day and this has been bugging me quite a bit, it's most noticeable while using WASD movement/no movement on mouse.
While moving in any direction (let's say you're holding W to go forward), hold down one of the buttons to fire a gun/do an ability attack. While holding that down, let go of W. Every time the gun/ability is on cooldown (and you're still holding that ability button), your character will keep running forward (or whatever direction you were initially holding).
It's a bit odd and appears to happen with all weapons/classes/abilities. It's frustrating to deal with while in the middle of combat.