Therefore not seeing a green browser lock nor being able to verify the certificate should ring alarm bells and could be considered a problem at least from an UX point of view.
It's a fair point that people feel more comfortable when they see a lock icon or the big browser bar while logging into a site. For the MITM attack reasons mentioned by CodesInChaos below1, SSL everywhere provides the most protection for your login session
and I can only speculate about why Stack Exchange doesn't use SSL to encrypt all pages (although there is an obvious economic issue to consider). See Nick Craver's blog entry about the issues around enabling SSL on Stack Overflow
In general, stack exchange caters to a rather technical audience; it's not uncommon for users to check behind the curtains when they have a concern. However, Stack Exchange is certainly not the only big site on the internet without a browser lock icon during the login process. Also, this question will be a useful point of reference for anyone worried about the issue going forward.
Does Stackoverflow use SSL when transmitting passwords during the log-in process?
There is no green lock in the browser when logging in.
While I can understand the fear you may feel in light of recent news, there are more sophisticated tools than the Firefox browser bar to validate whether a site is using SSL. One such tool is fiddler, or you can use wireshark if you prefer sniffing the directly.
These days HTML pages are complex, and unless you're going to an internet banking site (which depends on marketing trust), there is no guarantee that a plain browser icon means the authentication is not encrypted.
Fiddler / wireshark will capture everything your browser sends.
I use stack exchange's OpenID, and captured my HTTP and HTTPS sessions in fiddler. As you can see below, the authentication portions are using SSL.
I would also mention that SSL itself is no panacea, and there are some rather disturbing things that have happened with regard to root CAs being hacked and the general state of so many certificates being trusted by default.
Replicating the login UX flow...
As a side note, Martin obviously was able to see a browser lock when he was logging in, but when I go through this sequence, I see what Mad Scientist mentioned...
A) Go to stackoverflow.com
B) Select Stack Exchange's OpenID
C) Login form
1 While it is true that a login session without a browser lock icon makes you more vulnerable loosing your credentials to a local MITM attack on your LAN; that technically is not Stack Exchange's problem. That is a security problem on your LAN... either within your home, or inside your company. If Stack Exchange wants to be the best possible site, I think adding SSL everywhere would be a security improvement... Although it's again worth mentioning that SSL itself isn't a panacea.