You will get notified about new answers to the question you're just writing an answer to, but this only happens every 40 or 45 seconds or so. Then you can load these answers without losing your text so far.
Note that this has also be discussed on the general Meta site http://meta.stackoverflow.com: Can I see if someone is currently answering a question?
It seems to me that this has something to do with the inverted (?) color scheme you're using. Generally, the revamped system works like this:
There are two types of messages, inbox and notifications.
We’re fiercely protective of the inbox, making sure only actionable
things directed at you go into it. Comments, answers, a handful of
post notices, ...
I wouldn't call it a design flaw, just a plain old bug – this wasn't by design. You're absolutely right, the popup should appear where you clicked (it used to be that way; this was a regression). Fixed in the next build; thanks!
I'm quite happy with the idea of sketching a solution and posting that first before working on a full solution. But I would like to ensure that the reason for doing so is clear to all: that it is to avoid duplication/waste of effort and not as an attempt to be "first to post". So I'd like to have some examples of how this could be worded (along the lines ...
Believe me, the Great Big Orange Banner was infinitely more annoying.
 As a mathematician, I'm officially sanctioned one hyperbole per day. This was not it.
 And I'm prohibited Bad Puns. Tough.
This might not be exactly what you are looking but there is a feature for getting emails with inbox notifications from Stack Exchange sites.
In the page for posting questions, https://tex.stackexchange.com/questions/ask, there is a link to the dialogue for inbox notifications. The link is at the mouse pointer in the following screenshot:
You can also reach ...