Are they collapsed threads? there should be a small icon beside the subject of threaded mail to expand the thread.

Not sure what the icon you are referring to looks like. None of the threaded messages appear in the inbox. It is only when I search for the senders name that I can see the emails in the search pane.

I have no access to a mac, but on windows it looks like this

Alternatively have you installed the conversations add-on?

The symbol is the same as you show above and yes I have installed the conversations add-on. If I uninstall the add-on will it cure the problem and if so how do I remove it.

Thanks for your help.

Threaded messages do not appear as an independent new message because you use the threaded option, so the new message will get associated with the original message and could look like it is not there even when it is and you see it by either expanding the relevant thread; in your image the Bug 981996 has been expanded as the small arrow has turned black to show relevant threads or by removing the threaded view option or only showing unread.

Switch off the threading if you want to see new mail as a new message at the top of your list of incoming mail. View > Sort by > unthreaded Or use the options to display only unread mail or threads with unread. 'view' > 'Messages' > 'unread' View' > 'Threads' > 'threads with unread'

Or use the Quick Filter Toolbar sunglasses icon to 'show only unread message'.

I also have 'Conversations' addon extension and it does cause me a slight issue with 'marked as unread' emails. If the thread is expanded, collapsed and i read another mail and then go back to expand the thread it will no longer be marked as unread - the 'unread' will auto change to 'read' even though I have not selected the email.

However, if you uncheck 'View' > 'Conversation View' - only located on the 'Menu Bar', then it resolves the issue without having to uninstall Conversations. I can now expand/collapse the thread and the unselected unread email remains marked as unread so easy to locate using the options as previously mentioned.