This is a service entrance conductor Drip Loop and has limitations according to the NEC.

What is the minimum distance to the "loop"?

At a quick code clook-up, I would think this is covered by 230.24(B).

Is there a messenger wire there? I can't see one, so I'm guessing that (1) wouldn't apply, and this drop would be covered by either (2) requiring a 12 ft. clearance or (4) requiring 18 ft. if there's truck traffic.

Have I missed anything?

OK, I think I misread that first time. Part (1) applies to the loop so the minimum is 10 ft.

How high is this loop? From an upstretched arm, I'd guess around 8 ft. ?