Hi Barry,
To answer your 2nd question (posting cash and leaving unapplied cash on the record), the easiest solution would be to create a 'zero dollar' cash entry and apply it to the cash (with an unapplied amount) and the 5 remaining invoices, thereby getting all the cash applied and the invoices paid.
As for the first question, posting adjustments looks at the current, historical and matching files to determine if the adjustment transaction number has been used before for that customer. If it has then the error message you are getting will occur.
Perhaps print the Customer Transaction report for that customer, with the 'Applied Details' option selected. This will allow the matching file to be checked as well as current and history.
Does the error occur during entry, printing the adjustment list report, or posting the adjustment? There was an error with the adjustment list report but this was fixed back in a 2004, and posting was not prevented (it was a report-only problem).