I have the same problem, and none of the above suggestions / solutions have solved it so far.
When I installed the EOS Utility software from the bundled CD (version 126.96.36.199), connect the camera to the pc and open the Web Service settings, it tells me it needs to download an SSL certificate. It downloads the certificate, and then installs it on the camera (or so it says).
I then shut down EOS Utility, I remove the cable, enable wifi on the camera and go into the wifi settings menu. When I try to upload something, it asks to connect to a wifi access point, after which I get the message: "Invalid SSL certificate. Connect to a computer and correct the settings with the provided software." On the top of the screen it says: "Error" and "Err 124".
On my mac, I can find the certificate on the harddrive, under a folder called "/Applications/Canon Utilities/EOS Utility/RootCertification/000001". If I remove the "AddTrustExternalCARoot.cer" certificate file from that folder, connect the camera again, start up the EOS Utility and click on "Web Service settings" it can download and install the SSL certificate again, but I keep having the same problem with the camera giving me Error #124, saying the certificate is invalid.
My camera firmware is 1.1.2.
I've tried both the 188.8.131.52 and the 2.12.3 version of the EOS Utility, both on Mac OS X 10.8.2 and on Windows 7 64bit SP1. Both perform the same and do not solve the problem.
Am I the only one still having this problem? I'll try and call Canon's support line again next week. I live in Japan, so it's a bit hard to talk to them in Japanese. There's so little information about this error on the web, it seems like it's not a common problem.
Any help would be greatly appreciated!