Dust on sensor?

I took some long exposure sky shots tonight and discovered a few "stars" in spots that stars shouldn't be (in trees, on the ground, etc). Looking further, I noticed that the colored dots were in the exact same spot on all the images. The dots usually appeared to be red, and individually, they are indistinguishable from the dots that corresponded to actual stars. The dots were in the same spot, regardless of focal length, and only appeared when the exposure was over 30 seconds. Would this be caused by dust on the camera sensor, or dust in one of the lens elements? If its the former, can I just apply the camera's dust-delete data to the image and fix it?

They're hot pixels caused by long exposures. There's a feature in Canon cameras that lets you cancel it out. It works by after the image is taken it closes the shutter then takes another exposure the same length, then digitally removes them. Alternately you can probably fix them in batch mode in a raw converter I think, but i'd do them individually.

If you shoot raw then Lightroom does a great job of removing them automagically.

I'm assuming I can fix them with the RAW tools in DPP?

Yes, the Tools/Start Stamp Tool (Alt-S) in DPP is the thing to use.