Using Mail with both pop and imap accounts

I have a Q to better understand how the Mail app. works in Lion so there is better coordination among my devices and mail = I'd like to lay out how it is now set up and see whether or not I'm right about how to handle them - and how to do things better.
1.  I have a .mac account and no problems with it = if I read and delete on iPhone it deletes off iPad and computer fine.
2.  I have an email account that is an IMAP account but at another host [I use Mail to get email from it] - so what I think happens is that it's sort of the same thing but operating on that other host as an IMAP so that the same thing happens more or less - email comes in on all 3 devices and when I delete from one it deletes from others = but maybe not as fast because it's going thru the Mail intermediary.  My need/wish is to use one email program [Mail] to get all my mail and that's why this and others all go thru Mail.
3.  I have a 3rd account that is a POP account and can't be made IMAP because of the nature of the plan/host - in that I've noticed that I'll have 100 messages on my main computer and delete 75 of them but the 100 are still left on the iPhone and iPad = so far I don't do much about it but I hope/assume I'm right to think that if I know I've read and dealt with the 100 messages that if I want to I can just delete them all quickly off the iPhone or iPad...I'm not sure how to handle a Pop account to minimize all the hassle.
Does this seem like the right way to go or is there a better way to manage these 3 diff. accounts ???  I noticed some of the problem when I checked Mail on my iPad and saw there were loads of old emails 'unread' on it that I had dealt with on my computer so I knew things were out of whack.
Last thought = I do go to Synchronize all Accounts from time to time but really don't notice it makes a difference but maybe I don't understand tht either.
thanks much

Okay, it just fixed itself without me doing anything, or even quitting the program again. It still seems like a bug.
Andy

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