How do I avoid "message could not be moved to the mailbox Trash" on iOS 10?
Here's what I did to fix things...

(EDITED, BECAUSE PREVIOUS WAY DIDN'T WORK... EVERYTHING REAPPEARED)

Go in to settings > Mail > Accounts > (Account Name) > shut off "mail"

Force quit the mail app; force quit settings app.

Re-open mail app. It should not show any mail from that account. Force quit mail app again.

Then reopen settings, re-enable mail. Everything is re-synced. Re-open mail app.