I have a situation where my app is stating I have no unread emails when I would have, say 20.
I have 3 email account set up.
What I found is that when one particular account gets above a certain number of emails the icon will display a number, but it's always off by 40 emails.
There was something wrong with that particular account counter.
I removed that account and reinstalled and it's back up and working.
I have just read a way to get rid of this........
Hold down Home button
You will see a bar at the bottom
Press left icon (looks like a pie chart)
Next window that pops up should ne RAM manage
Click clear memory and that should work.
Did for me