Mail.app performance after upgrade to Lion

I had a similar problem in Mail on Mountain Lion, where attachments did not show up for a message. When looking at the raw source (⌘⎇U) of the message, I also found that headers of the message were missing.

I managed to fix the issue by selecting the mailbox containing the broken email, and then using the "Rebuild" command from the "Mailbox" menu. After a short time, my emails reappeared, complete with attachments.

Judging from your description of the issue, it seems that Lion’s Mail.app has difficulties correctly executing a move AppleScript action on a PO3 server (or maybe just your POP3 server – not having a POP server to test myself, I cannot check). A solution could be to separate the two components of the move operation by replacing the line

move eachMessage to mailbox "Archived/BTR Monitoring Emails"

with

copy eachMessage to mailbox "Archived/BTR Monitoring Emails"
delete eachMessage

in the hope that an express deletion command will fare better. If that doesn’t alleviate the issue (because the deletions suffer from the same issue – I can’t say for sure from your question), you could also try setting the delete status of the message instead of sending it a delete command, i.e.

copy eachMessage to mailbox "Archived/BTR Monitoring Emails"
set deleted status of eachMessage to true

though I’m not entirely sure how that will go down within a POP server (it sounds like something designated for IMAP).

Finally, you could try commenting out the set read status of eachMessage to true lines in the filing and deletion blocks – this should, by rights, not affect the server, as POP3 has no notion of a “read status” (you need IMAP to store that server side), but it might conceivably be an issue if Mail’s AppleScript thinks otherwise. Setting the message status to read can also be achieved within a rule without resorting to AppleScript, so removing this from the script should be a non-issue.