The problem appears to have been fixed:

what the Players engineering team believes is a fix for this issue has been pushed to our production servers.

YouTube has acknowledged the issue:

There’s definitely and issue, presumably due to last night’s push, and we’ll get it resolved as quickly as we can. Thanks for bearing with us while we investigate.

We’ve had a few folks reporting in the support forum that YouTube videos are freezing after playing for about a minute. The issue appears to be on YouTube’s end, and they are aware of the problem. Here are a few resources on the subject:

We recommend starring the bug report to both get YouTube’s attention and track updates to the fix. We will update this post as the topic develops.