Is there anything outside the solar system I could watch moving?

I mean, not just in successive images taken over years, months, or days, but within hours or minutes. If someone gave me use of an observatory optical telescope for a night, is there any star system, nebula, etc, I could point it at and see a noticeable change over the course of the night?

No.
Nothing is moving fast enough and is close enough to us to perceptibly change in years, let alone a single night.

The biggest effect would be the motion of the Earth around the Sun, causing parallax, but even that is far too small an effect to see over one night.

Pulsars are probably your best bet. They can spin many times per second. Unfortunately, you’re not going to see that with an optical telescope.

Given years, you could probably watch the light ring from a supernova expand.

I wonder if you could see Neptune move in just one night?

Barnard’s Star moves approximately 10.3 Arc Seconds per year; the Moon is about 1800 Arc Seconds in size as seen from Earth.

http://en.wikipedia.org/wiki/Barnard%27s_Star

Do any binaries revolve around each other fast enough to see?

Good point; some binaries have periods as short as a few hours (w UMa, with a period of ~8 hours, comes to mind). They’re not separately resolvable, but you can see a change in the light output when they pass in front of each other.

There are some visible-light pulsars.

Yes, you can. Every once in a while, various planets and other solar system bodies eclipse a distant star. These are usually predicted in advance. You can point your telescope at the star at the right time and watch it disappear behind the planet or point it at where the star should be and watch it reappear. In fact, they use such occultations to measure the diameter of small bodies (asteroids and Kuiper Belt objects) with more precision than other methods. These occultations usually only last a few hours at most.

There are several types of variable stars that have periods on the order of hours and changes in brightness on the order of one or two magnitudes: such a star would show changes in brightness of over 100% several times over the course of a night.

Neptune is not outside the solar system.

I was going to suggest dwarf cepheids, but I don’t think they match the OP’s criterion of “moving” and I’m not sure if the magnitude changes can be spotted with the naked eye.

I’ve heard stories of desert cultures testing observational skills by having a person look at the night sky, putting the person in a tent, and bringing them back out a few hours later and asking them to identify what has changed. No idea if these stories are true but it’s a great concept.

I assume by this you mean “what has changed relative to each other,” not “what has changed relative to the horizon (or the zenith),” because the latter would be pretty obvious.

After they excluded Pluto, if they do it by distance from the sun guess who is next :eek:

Pluto got kicked out of the planet club but continues to hang out in the solar system,

Correct - they were looking to spot moving planets and/or variable stars.

But distance is not why they excluded Pluto. Size matters.:eek:

The stars orbiting the black hole at the galactic center move pretty fast but it’ll still take you months to notice:
From UCLA