Most of the problems I've seen with people saving EPS files out of Illustrator 10 involve problems associated with going over a network, or to some kind of removable/external drive.
If not saving locally, try it there and see if it works better that way... This may reveal some kind of network problem.
If saving locally, this can also be caused by damaged permissions in OS X. You can try running the permissions repair utility (located in the Applications>Utility folder there is a "disk Utility", with a permissions repair option on the "First Aid" tab.)
This utility isn't always 100% successful though, so it might be a good idea to try logging in as a new user on the system, (Make sure the new account has admin rights).
Jon
Dick
As to your cross-platform question... If your other user has AI 10, it shouldn't matter whether or not they are on Mac or PC... As long as you give them a file that a PC can read, the .AI format is the same on both platforms... So the PC should be able to open it.
I've never seen a "dotted" bounding box before... But you can turn off the regular bounding box in the "view" menu. "Hide bounding box".
Dick