I was trying to install Call of Duty 1 (in Steam installed trough PlayonLinux), but every time I try to run it I get a buffer overrun.
I can’t help directly (Google may be your best bet here). As an example, a quick search did turn up the following (but only relevant if you have ATI graphics hardware
http://www.overclock.net/t/767175/cod-buffer-overrun-fix
*Essentially, it was mentioned that atioglxx.dll was required. (It can be found easily enough with a search if required.)
Otherwise, I suggest you post in the Steam or POL forums perhaps
http://steamcommunity.com/app/2620
http://www.playonlinux.com/en/forums.html
No, I’m using Intel graphics. Also the file they linked to doesn’t exist.
It won’t then. That’s why I mentioned ‘if you have ATI hardware’ 
Consider posting in the games forums I linked to. Good luck.