Well, splitting the database and pushing the Front Ends to the Desktops of the users did eliminate the "...not have exclusive access..." errors.  However, perhaps because my AutoExec macro opens 6 tabbed forms, some of the users are getting errors that say, "Cannot open any more databases."  I have urged the users to close a couple forms and that seems to help, prompting me to think the local front ends are bumping into memory issues.  Is there something I can do besides opening fewer forms with the AutoExec macro?
And, my department head really liked the single dB that worked fine for us for 6 years until I updated all of the tables by moving them into a blank 2010 (still 2007-style?) database. I am recreating empty tables in an older, emptied, backup file without importing the newer-version tables.  I hope I am on the right path to get away from the newer-version tables that seem to have caused the "...not have exclusive access..." errors.  Advice or suggestions?

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Reply from Alex Hedley:

I've seen this a couple of times on the Forum recently, it should be when a large number of objects are open, I wouldn't expect it at 6.
Was the db compact and repaired before distributed?
Does it compile fine in the VBA Editor?
Are they having memory issues?