If two users go to the "Print Checks and Forms" screen, they both will have the same check number shown as the first check number to use. This causes a duplicate number to be used for two different check prints. Is there a way to prevent a duplicate check number when more than one person is using the Print Checks and Forms at the same time?

I'd doubt it - sounds more like a process/user problem then a NetSuite problem. Why would two people be printing checks for the same account at the same time? Seems like a recipe for "I picked this transaction and it didn't print"

They have multiple bookkeppers who issue refund checks to customers.

Could pretty easily be solved by people telling one another "hey I'm doing a check run" and "hey I'm done with check run"