"If so is there a way to remove these entries from the found set without it being permanent?"
Found sets are dynamic. You can use different find requests to pull up as many different groups or records as you need. None of them are "permanent".
To exclude those records missing an email address:
Enter find mode.
Enter the criteria you need to find your group of records.
Enter a single asterisk (*) in the email address field
Perform the find.
What do you mean by "without being permanent"?
You can always open a new window, find the records that do not have email addresses and contrain the found set. Then you can try to send your email, and when done you can close the window and go back to the orig window which has your orig found set.
As it turns out even though filemaker pro 10 said it was unsuccessful in sending the emails, I just received a response from that mailing. Does this mean its a bug?
Since you sent out a bunch of emails. I assume some where successful and others, probably the ones missing an email address, did not.