A: Make sure everyone has the Flash Player
installed. Also make sure that when you're exporting the .swf from Flash that you set it to export at the lowest common denominator; if everyone is running really old systems, make sure to export the .swf for version 5 Flash player.
B: Make sure there are copies of all your components to your project's library before you export the file to .swf
If you can absolutely guarantee that both these requirements have been met, then I have no idea
All the best,
*edit: missed an important bit...