Thanks for posting your issue, it gives us the opportunity to look into things and fix these error messages. There are two issues in this thread I would like to address. The HTTP intercept issue brought up by the previous poster is definitely not related to a Gogo flight. That route and aircraft type are operated by a different company, and customer care is offered directly by the airline. Gogo does not use any technology to intercept your HTTPS traffic.
As for your error messages and inability to browse certain sites, this is most likely caused by your IE configuration, which could include a proxy server setting. We would love to help look into this. If you send me a PM, I would love to make this right and will get you in touch directly with a customer care expert.
Thanks,
Scott@Gogo