Besides clouds, inclement weather and high-flying airplanes, what other interferences must astronomers contend with in the night sky?
Clouds and weather are two of the big ones, and you mentioned those. Another important problem is light pollution--light that comes from (generally manmade) sources on Earth that interfere with your observing. Don't build a telescope next to a big city or you'll have this problem. You also might have problems if you observe during a meteor shower, or if you're observing near a really bright planet like Venus or Jupiter. And then of course there's the Moon, which can complicate observations of anywhere in the sky.
Edit by Michael Lam on November 21, 2015: There are interference sources in all parts of the electromagnetic spectrum. In the radio, astronomers have to contend with man-made radio sources (cell phones, wireless internet transmitters, etc.). At submillimeter and far-infrared wavelengths, water in the atmosphere blocks our view, so telescopes are built in high-and-dry locations, are onboard aircraft, are launched into space, or may even be put on ballistic rockets. Telescopes observing very short wavelengths, such as far-ultraviolet, x-rays, or gamma rays, are exclusviely built in space because they can't see through the atmosphere altogether.
This page was last updated on November 21, 2015.