The latest patch for the game (v1.2) can be downloaded from the Files section.
The patch is available in English, French, and German.
A launcher for the game that enables support for widescreen and high resolutions (beyond the 1024 x 768 supported officially in the game) is available here. The launcher must be set to run in Windows 7 compatibility mode in order to work.
For many people, the version of Installshield which MechWarrior 3 uses refuses to start, and instead just hangs. This appears to be caused by conflicting programs running in the background. Singling out which program this is can be quite difficult. A simple workaround is to create a new account with administrative privileges, and install MechWarrior 3 under that.
Alternatively, open task manager, go to details tab, right click setup.exe, click "analyse wait chain", tick both boxes to end both processes. Repeat these steps until setup launches.
The following methods apply to both MechWarrior 3 and the Pirate's Moon expansion pack (except for the official patch step, as none were ever released for Pirate's Moon).
Compatibility mode (Windows 98 / Windows ME)
Use a tool like Rivatuner to limit the game's framerate to 30fps. Enabling V-Sync helps too.
Programs and Features
Turn Windows Features On or Off