Try turning the account off and on : Settings > Mail, Contacts, Calendars , then tap the account on the right, slide Mail to 'off', exit settings and go back into the Mail app, and then go back to Settings and slide Mail back to 'on'
If that doesn't work then try closing the Mail app via the taskbar : from the home screen (i.e. not with the Mail app 'open' on-screen) double-click the home button to bring up the taskbar, then press and hold any of the apps on the taskbar for a couple of seconds or so until they start shaking, then press the '-' in the top left of the Mail app to close it, and touch any part of the screen above the taskbar so as to stop the shaking and close the taskbar.
Another option is a reset : press and hold both the sleep and home buttons for about 10 to 15 seconds (ignore the red slider), after which the Apple logo should appear - you won't lose any content, it's the iPad equivalent of a reboot.
If you still can't delete them then go into Settings > Mail, Contacts, Calendars, select the account on the right-hand side of that screen, select Account, then Advanced, Deleted Mailbox, and under On The Server tap the 'Trash' folder so that it gets a tick against it - then come out of that series of popups by tapping on the relevant buttons at the top of them and then see if you can delete emails.