Could I build an airship (rigid dirigible) that used a vacuum rather than lifting gas?
what are the technical or mechanical limitations to doing so?


There is no known material that has a sufficient combination of lightness and strength to support a vacuum that would support the weight of the container on Earth at sea-level. 

There was a similar question with a good answer on Physics.se 


Beryllium Vacuum Sphere Boat/Aircraft



  Is it possible to make a solid rigid evacuated "balloon" out of Beryllium or other elements or alloys?


The currently first answer runs through the maths 


  calculated it over a database of almost 3700 materials including all common aerospace composites, metals and alloys.  


and concludes


  So in short, the best materials fall short of achieving our aim by a factor of just over 2. It is conceivable we might push up the stiffness / density ratio by perhaps developing some kind of Beryllium foam. For example, a closed cell foam of this Beryllium with a relative density of 0,041 would give a value of about 920 at the expense of lowering the Young's modulus to about 600MPa - however, I have no idea if such a foam is even possible. Alternatively it might be possible to come up with some clever engineering of the envelope geometry to overcome the buckling constraint. However, I suspect the effort is unlikely to pay off with a better boyancy ratio than is already achievable by conventional balloons.


Other related questions 


Is it possible to create a vacuum ballon using concentric partially pressured spheres?