Are boom microphones designed to only capture dialogue? If not, is all extraneous noise filtered out during post-production? How is this done? How was this done before computers?
What you are calling a "boom microphone" doesn't really exist. The boom is a pole that holds a microphone so that the operator can stand outside of the frame and still get the microphone into a location from which it can pick up sound. Microphones come in many different styles, as defined by the way they sense sound signals and the directions from which they will pick up sound waves. Usually, booms are used with a "shotgun" style of microphone. Shotgun mics are designed to be the most unidirectional mic, which means that they pick up sound waves that are coming from sources directly in front of them, while sounds that come from the sides and back are hardly noticeable. The side and back sounds are usually further reduced by the use of a "dead cat" or wind cover (which you've probably seen pictures of... They look like a stuffed animal fur wrapped on the mic.)
What this means is that the booms are used to point the shotgun mics directly at the talent so that the mic picks up the dialogue and as little ambient sound as possible. If there are sounds that are still recorded and no usable takes were made, then ADR (Automated Dialogue Replacement) is performed. In this process, the actors are put into a sound recording studio and they re-record their lines while watching the recorded video footage. That way a clean audio recording is made. This can be mixed with the recorded ambient sounds so that it fits with what is recorded on location.