[SalesForce] System.CalloutException: Unable to tunnel through proxy (Winter ’16 issue)

This morning I'm seeing sporadic failures across the board for our various integrations in production. When using HTTPRequest callouts, a System.CalloutException is being thrown with the following message:

First error: IO Exception: Unable to tunnel through proxy. Proxy returns "HTTP/1.0 500 Internal Server Error"

And less frequently: First error: IO Exception: Connection reset

This is popping up on webservice callouts that have been working without issue anywhere from a month to 2 years. We are not making any of these requests through a proxy. Some requests to an endpoint fail with this error, and I see several seconds later another request that succeeds. I have opened an urgent ticket with Salesforce, although they have yet to respond.

Are we running into some limit with concurrent requests that I'm unaware of?

Update: Salesforce support says others are reporting this as well, and R&D is looking into the issue.

Update: This issue is now listed on https://trust.salesforce.com/trust/instances

Update: The Salesforce Technology Team has identified a fix for the issue causing intermittent errors with Single Sign-On logins and outbound HTTP calls. The fix is currently undergoing testing prior to deployment. Deployment will begin once the testing and validation is completed. Please check the status of trust.salesforce.com frequently for updates regarding this issue.

Final Update: The Salesforce Technology Team has resolved the performance degradation affecting multiple instances for the issue causing intermittent errors with Single Sign-On logins and outbound HTTP calls. The problem began at 13:00 UTC and was resolved by 21:38 UTC.