This one is subjective. To some, just finding an abandoned spaceship would be spooky. I'll say there's probably not a lot that has to happen to evoke this feeling.
Actually, unless your spaceship never had a breathable atmosphere or the atmosphere was vented before the spaceship was abandoned, rust is totally possible on the inside and even the outside. As the oxygen escaped, rust would be produced on any exterior iron in contact with the venting oxygen.
If you're in orbit of a planet with an oxygen atmosphere, the trace amounts could also cause some amount of rust over time.
Here is an example of [apparent] oxidation on the Quest Joint Airlock thermal cover:
As Tristan pointed out in the comments, the coloration is not actually oxidation:
the discoloration on the airlock hatch cover is most likely not oxidation but rather contamination due to outgassing from materials that become volatile in the space environment (plastic, rubber, trace organic compounds in the interior atmosphere that get released when the hatch is opened, etc.). The brown color is from the contaminants being altered by UV radiation. To the extent that oxidation is occurring, it would act to bleach the discoloration, rather than contribute to it.
Despite that, you can still see both that oxidation occurs, and that even if it wouldn't look like you imagine, there are other effects that can cause a similar appearance to rust on Earth.
Aside from actual rust, when the coating and lubrication breaks down on metal parts, they will cold weld together. Steel will develop crystallographic defects and a positive charge.
In the short term, this depends somewhat on where in space you are, but we're talking about an ancient spaceship. By that point, it's almost certain that its going to be battered by cosmic dust. Here's an example of what debris damage might look like:
A lot of parts will become discolored overtime by radiation exposure. Does that count?
It might be hard to visualize this on other parts, but here's an example of UV effects on rope (the rope on the right is new, the left is affected by UV):
If your spaceship is in orbit of a planet, you'll probably have even more junk to run into. I just hope you don't expect the thing to be operable. For that matter, if your spaceship is in too low of an orbit, then its orbit could decay and it could break apart rather quickly due to interaction with the atmosphere.
You didn't ask, but the spaceship might also get moldy, see this question:
Melanized fungi on the ISS - are they 'enjoying' the elevated radiation levels there?
However, the fungi would require at least minimal levels of oxygen, so I wouldn't expect the mold to last long on an abandoned ship.