Do you use a detection routine in your code to see if Flash is installed? A lot of the detection code that gets used out there doesn't work right with Macs - one good example that I saw last week was the personal site of the wrestler Diamond Dallas Page (
www.ddpbang.com). The site displays properly on Windows IE, but the detection routine stalls on an OS X browser (any of them), leaving a blank spot in mid-screen where the intro is supposed to play. Flash, OTOH, is installed fine under the OS. And it can be manually coaxed into playing, as well.
Odds are it isn't a server problem or a client problem, but a glitch in your procedure for checking. Flash 5 and prior generally works fine on a Mac. The user should make sure he has the latest version of the plug-in installed, though, and delete earlier ones if present.
The Macromedia support groups may be a good resource for you here, too.