If an alien probe is still active it might be detected emitting heat. Or, it might have an unusual composition that would stick out in multispectral mineralogical mapping. The buried alien monolith in the sci-fi classic film "2001: A Space Odyssey" had an anomalous magnetic field. (As so do some locations on the moon!)
Mars is being photo-mapped to but not yet to the exquisite resolution of LRO. My fantasy would be to see something like the soon-to-be-launched Mars Science Lab, Curiosity, comes face-to-face with an alien robotic explorer camped out on Mars. The two robots gaze at each other as their artificial brains search for any algorithm that tells them how to proceed in the presence of another machine.
An extraterrestrial race that goes to the expense and complexity of dispatching a robotic emissary to visit here would face the risk of the probe being found, captured, dissembled, and put on museum display. Therefore, I think that any probe would be designed to be stealthy to ensure its long-term survival. Hiding out among the asteroids might be a good strategy.
What would the reaction of a mission science team be if something blatantly artificial-looking popped up in a routine photo survey of the moon, Mars or an asteroid? Would it be kept under wraps? Or would there be a new space race among countries to go salvage the artifact and bring it back to Earth? This would certainly bolster funding for solar system exploration!
But it would be as eerie as Robinson Crusoe finding Friday's footprint on the beach of a deserted island. We would at last know that we are not alone in the universe, but we would have no clue to the probe builders' identities, location in the galaxy - or any motives beyond simple curiosity.
Images: Top – NASA's Mars Phoenix lander as seen from orbit (NASA); Middle – The backshell of one of the Mars Exploration Rovers litters the Martian landscape (NASA); Bottom – The long shadow of the Surveyor lander on the moon (NASA).