This is similar to the error I get with NodesAsTabs (which accesses $visitor['user_id'] to trigger the error). But the above error doesn't show my addon in the trace. That trace is pure XenForo and it's giving a similar error.
Since there are no addons in play I am moving this to bugs so the devs can review it.
A hint for add-ons that may encounter this (I've had similar issues with my own add-ons).
The $visitor info generally is not set (so every index is undefined) on pages where the session isn't needed. Examples include proxy.php, deferred.php, css.php, and some other situations. So the user_id undefined error can potentially occur a lot in those situations. But it's hard to reproduce on demand, because in general those scripts either cache results or only run occasionally.
While the backtrace doesn't show an error, it's certainly possible -- and indeed likely -- that an add-on is interfering. For example, any add-on that manipulates the visitor object or any query used to create the visitor object could cause this.
If it's still happening, you'd definitely need to disable add-ons to try to narrow down the potential cause. I would guess that there's potentially some sort of query modification happening that is interfering.
I had 4337 pages of these errors over 6 hours last night. Troubleshooting is extremely difficult because the errors come in waves - I hadn't had any for at least a week prior to this. So I'm not sure how to tell where the problem lies by disabling add-ons due to the episodic nature of the issue.