If you were having server or network trouble, I would expect to see the crashes equally distributed over all computers, not just 3 specific machines.
Since the crashes only occur with specific machines, that suggests that there is an issue with those machines.
Try creating a new user account on one of these machines and have your user use that user account for a while and see if they still get crashes. If the crashes go away with that new user account, repair or replace user accounts on the problem machines.
Use a hard drive utility to check the problem machines over for any possible issues.
Remove the Filemaker Preferences file on these three machines by dragging that file out onto the desktop. FileMaker will create a new Prefs file the next time you open it on that machine and this is an old "cheap fix" to try with software trouble on a mac.
If all else fails, try re-installing FileMaker and Bonjour on each of these computers.
Thanks for the quick reply PhilModJunk... I will try those solutions and post back here in a week with the results.
Activity Monitor in Utilities in Applications can be set to display System Memory in the Dock.
Console in Utiliites in Applications can display Error Logs for many processes and can be difficult to decode.
Directory corruption is normally repaired with Disk Utility. It cannot be run on the Boot Drive from the Boot Drive in the Finder.
Will be run when Safe Booting [Shift Key down]
Can be run from Terminal as fsck (file system check)
AppleJack can run it from Single User Mode.
Do the three affected computers have anything in common.