This is a known issue logged by Apple, and here is a Knowledge Base article that goes into the details of the resolution:
Your iPhone, iPad, or iPod touch may not always update when you read, delete, reply to, or move messages in MobileMe Mail, or in an email application on your Mac or PC.
iPhone, iPod touch, iPad, MobileMe
If your MobileMe Mail account is configured to use Push (in the Fetch New Data settings on your device), your iPhone, iPad, or iPod touch will automatically update to reflect the status of your MobileMe mail only when you receive a new message in your Inbox at your MobileMe email address.
Push notifications only work for new emails delivered to in your Inbox, not email read status.
Here are some examples of when you won't see messages automatically updated on your device:
You should get a Delete button on all of your devices.
To resolve this issue go to Settings > Mail, Contacts, Calendars > [affected account name] > Advanced > Deleted Mailbox on iPhone or iPod touch.
If "On the Server" is an option, select Trash below that (or select Deleted Items or Deleted Messages). Otherwise, select Trash located under "On My iPhone". Once the Deleted Mailbox has been set, tap Advanced and then press the Home button to return the Home screen.
If the Deleted Mailbox is already set to Trash, please follow these steps: