I've been getting the same thing. When you click the STO shortcut and the sign-in/patcher window loads up... it's just a web site in a window, pretty sure it uses IE controls to render the page since they use visual C++ 8 runtimes...and the SSL dialog is the familiar IE/windows one.
I created Atari Ticket #1102506 - Just want to report it in the forums in case there is any disconnect between Atari support tickets and the developers of STO.

I work for a large corporation famous for making copy machines..... anyway we were bought by them and I don't care what they say here... there are always disconnects up and down the line, we have plenty of our own... to be supportive, I expect to be proven wrong
Atari Ticket Summary:
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I keep getting SSL certificate problems when opening the STO loader... Something like this makes me feel nervous that the page we enter our account credentials in is not as secure as it should be. This has happened to me on more than one computer so I don't think its a problem on my end.
When clicking the Star Trek Online Shortcut the normal window appears, but is white with the text at the top saying "Loading, Please wait." Then a dialog appears titles "Security Alert" it says "Revocation Information for the security certificate for this site is not available. Do you want to proceed?"
I have created a screenshot and uploaded it to an image hosting site:
http://i52.tinypic.com/1zgtftf.jpg
I viewed the certificate details, look legit:
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Issued To: *.startrekonline.com
Issued By: Go Daddy Secure Certification Authority
Valid from: 2/22/2011 to 2/26/2012
Issuer Info.
SERIALNUMBER = 07969287
CN = Go Daddy Secure Certification Authority
OU =
http://certificates.godaddy.com/repository
O = GoDaddy.com, Inc.
L = Scottsdale
S = Arizona
C = US