>> If a starship composed of a 1,000 kilometer-wide sail being pushed
>> at nearly the speed of light by a very powerful laser beam in the
>> terrawatt range was headed towards Earth - and was, say, less than
>> 1/2 a light year away - how would it appear from our planet in
>> various spectrums and wavelengths, especially optical?
I'd expect some leakage through the sail and some scattering of light from the back side, plus some of the usual specular reflection as well as diffraction around the edges of things such as shroud lines and the payload. So a great telescope pointing in the right direction might see a point of light with a spectrum matching that funny stellar spectrum anomaly Anders mentioned.
If it is a decelerating sail-within-a-sail type, as some have speculated on (outer ring is a separate mirror to bounce light back at the central sail) there might be two points of light, and the smaller sail is being illuminated on this side. Might be bright if you were looking from the right place. If this laser light is strong enough to cause rapid deceleration, it might be bright indeed.