First you have to understand one thing. I'ts the very fact that Doom 3 is over an decade (10 years) old and was made with Windows 98/Me/XP compatibility in mind .
Issues on newer systems are inevitable and in the end some are indeed present.
Mostly for ATI/AMD graphic card users. Some will notice graphical glitches other won't be able to run Doom 3 at all.
Below in few simple steps i will introduce you to a simple solution on how to fix those issues.
Go to Doom 3 main directory by either right clicking on the desktop icon and selecting find location/go to location, or by My Computer/This Computer.
There find file named "Doom3.exe" and rename it to "Doom 3.exe".
Create new shortcut to the desktop by right clicking modified file and selecting: Sent to > Desktop.
Or edit all paths in existing shortcut to reflect changes made to the executable file. Add spaces between Doom and 3 in both path boxes. Or just go with the easier first method :P
That's all. Adding one space into a file name fixes most of the issues for ATI/AMD GPU users.
I decided to upgrade to Win10. New official (retail, not internal build) build was released. Works flawlessly. So I wanted to confirm that this method and overall Doom3 runs on Windows 10 without issues.