I intended to ask about actual IMAP bugs. Things that go against the RFCs.
Showing the gmail labels as flags would be legal by the protocol (and have some disadvantages), showing them as mailboxes also legal (and have some other disadvantages), so I don't count that as a bug, it's merely a situation where one has to choose disadvantages.
The duplicate notifications are different; the way IMAP is designed the server cannot know which TCP connections originate from the same client. It can guess based on IP address and some other things, and it can know something based on RFC 2971, but 2971 also says explicitly that the server shouldn't do anyhting differently based on that. Which has been discussed in one of the IETF WGs, and the consensus was that the server isn't permitted to suppress probably superfluous notifications. If a client opens two connections, getting rid of duplicate notifications is the client's job.
www.rfc-editor.org/search/rfc_search_detail.php?author=gulbrandsen are my RFCs; I actually wrote most of those and gmail implements four of the IMAP-related ones I've written.