Hoping this thread is appopriate for this:
I've followed the method in the Wiki FAQ of bookmarking the customized URL for check-in with my name and confirmation ABC123. Now if you enter it early, that URL no longer appears in the address bar, but there's an error form with fields populated to correct the information. I changed the confirmation code at T-24:15, and got the check-in screen with Status: Security Document Available. I figured I could keep refreshing that and it would eventually change to Boarding Pass Available. When T-24 had passed according to time.gov (no more time stamp from WN to tell me their time), the status didn't change; I made one attempt to move forward and it only offered the security document. I then went back to the screen to enter the code, past 30 seconds in, submitted it, and got Boarding Pass Available.
Based on this, I wonder if I'm better off checking in from MySouthwest. Also I've been e-mailing myself the customized URL; it's been nice just to click on it, especially on the return when I'm out and about and can do it on my iPod Touch. I'm wondering if that will work, since the URL in the address bar changes completely.