I have a strange problem that affects nearly every first person shooter I have tried. When I click the left mouse button the camera spins around. In some games the camera jumps to a random location, in others each click causes the camera to turn slightly.
I fixed this in Half Life 1 & 2 by turning off raw mouse input, however, the camera will still spin out of control if I move the mouse near the edge of the screen while holding the left mouse button. This problem affects games run under wine. The Doom 3 linux client is not affected, while the same game under wine is subject to this problem. Games not affected include Quake running on darkplaces and Duke Nukem 3d running on eduke. I have tried another mouse and the problem persists. I am running Netrunner on an A4 APU from AMD. Any help would be greatly appreciated.

Please specify (because it is not clear) if this is only for games in wine or native Linux games also have that problem. In winecfg you should select "Automatically capture the mouse in full-screen windows" in "Graphics" tab. Try also installing DirectX by winetricks.

Sorry, I should have been more clear. Half Life and it's add ons, Half Life 2 and it's episodes, Left 4 Dead 2, Portal, and a game called The Talos Principle are all installed native on Linux through the Steam client and ARE subject to this problem.
Quake running on Darkplaces, Duke Nukem running on eduke, Quake 4, Prey, And Doom 3 are all native and are NOT subject to this problem.
Doom 3 and Halo in wine ARE subject to this problem.
I will try the things you suggested when I get home. I forgot to mention that my Asus laptop with Intel graphics running Linux Mint 17 Mate is not subject to this problem despite running the same games. I am thinking about booting up Mint on my problem desktop to see if the issue persists. I will update when I have more information. Than you and have a good day.

Okay, I had already set wine to capure mouse and directx did nothing.
I booted up Linux Mint 17 Mate from a flash drive. Unsuprisingly, something went wrong.
Halo would not work, I just got a black screen on the menu and I did not have time to fix it.
My Steam games wouldn't work without Steam installed and I had neither the time nor the patience to do so. I got lucky in the fact that I have Urban Terror, so I was able to run it under wine. It did not seem to have the aforementioned problem, though I still need to run some more tests. I made the mistake of running the Urban Terror updater and it is downloading at the speed of eventually, so further testing will have to wait. Looking at it now, it would seem to have frozen up. Yay.
So I will test further when I have time, presumably sometime in the next couple of days.
On a more philosophical note, if Linux Mint is free from this issue, I am going to have to seriously consider switching. This version of Netrunner is from the beginning of the year and no longer seems to be getting updates, so I do have plenty of incentive to do so.
I just don't look forward to backing up all my games. Better now than later I suppose.
I can't help but wonder though, what exactly is causing this issue. It may very well be limited to this release of Netrunner, which would explain why I cannot seem to find any information on this problem.
Sorry for the rambling, I have a lot of junk rattling around in my head at the moment.
I just restarted the updater. Fingers crossed. Good day.

Very sorry for the late reply. I have been very busy and have had no internet access in a couple of days. Further testing with Linux Mint and Urban Terror seems to suggest that this problem is limited to Netrunner. When I get the chance to install it, I will post a final message. Not sure if I can mark this thread as Solved, but if so, then I shall do that as well. Thank you, good day, and good luck to anyone who comes across this thread looking for answers.