When a user disables tabledrag, a cookie is set, disabling tabledrag on every page on the site. For someone who was just playing with that link to see what it did (most common use case) this creates a less-than-ideal experience and bad impression of the software.

What we really need instead of a cookie is a setting. People who want tabledrag disabled permanently should use the setting. People who need to disable it temporarily will use the link.
Recent comments
Thanks, the /tmp folder was the problem. I moved it elsewhere and then the updated worked. Thanks again!
Update 1.35.1 appears to install but hasn't
Probably not the reason, but worth to do a quick check: Sometimes the update cache interferes, so if something's odd with updates - some module (or core) claims to have updated, but then...
Update 1.35.1 appears to install but hasn't
Nope, not touched any permissions!
Update 1.35.1 appears to install but hasn't