The email I have sent from my mac mini does not show up in my email on my ipad1.

Emails you are sending to yourself, or emails not showing up in the Sent folder? I'm going to guess the second.

If you want the Mac Mini and iPad (using the Mail app on both) to have the same Sent mail box, then go into Preferences in Mail on the Mac, choose accounts, your account, the Mailbox Behaviors tab, and make sure you've got Sent set to be stored on the server.

This works for both MobileMe and Google. It should work with any IMAP email service, but YMMV.

You can also set Junk, Trash, and Draft to be on the server.

Note that your old Sent mail folder will be moved to the On My Mac section. If you want those emails on the server you will have to move them manually. However all new sent messages should show up in the right place.