Are airships useful on Mars?

Yes they are potentially. You can have an airship in a near vacuum. Several ideas for balloons for exploring Mars. This is project Archimedes - a 2009 mission by the German Mars society which never flew. Also, the Solar Montgolfiere Balloons for Mars. read more

Well, though I don't think they have any such ambition - the atmosphere at this height is roughly comparable to the Mars surface in density. So - if it worked out - such airships could land on the Mars surface and take off directly from the Mars surface, no need for any intermediate steps. read more

The "airship" would actually have to be a vacuum ship, that is, a rigid vessel with a vacuum pump to keep the air pressure inside near zero. Altitude could be controlled by slightly increasing/decreasing the amount of trace gas inside. read more

A vacuum airship would be a valuable design for a vehicular probe for Mars. There are far fewer obstacles for an aerial vehicle as compared to a land vehicle such as existing Mars rovers, e.g. one need not worry about the vacuum airship getting stuck in a trench or being unable to traverse terrain. read more