Just hit across this issue when testing something else. The side-effect is that you will be unable to stay logged in.... (or register for the cloudbees free plugins)
Seems to be a bigger effect in 1.475 though may be affecting other versions. Clearing the cookies for the Jenkins server hostname resolves the issue (as the request header size is then less than 4k) But for some reason my cookies keep on accumulating. May only affect Chrome as a browser
