When I have cleaned out my Mail InBox on the iMac down to about 5 messages and open Mail on the iPad and iPhone all the 30 other unwanted emails are still there?
iPad, OS X Mavericks (10.9.1), iPad3 and iPhone 5
Sounds like you are using a POP3 email account rather than an IMAP account. POP3 accounts will not sync changes to your other devices. If you want to be able to do that, you'll have to use an IMAP or exchange email account. iCloud email, Gmail and Yahoo are examples of IMAP accounts.
Trouble syncing Mail on iMac with iPad and iPhone
