The newspaper article says that Jasmine's last name is Devon, but dialogue and other material throughout the episode, including the cover of the magazine, say her last name is Delancey.
The flag on the mailbox at the Lake House was always up. One raises the flag on a mailbox to indicate to the mail carrier that there is outgoing mail in the box. The mail carrier will then take the outgoing mail and lower the flag on the mailbox. But there was no outgoing mail, nor did the mail carrier lower the flag once he delivered the mail (on two occasions).