A fun little ship?

What is the smallest boat that could be built to reliably support a full ship rig?

What if you want a crows nest/ lookout?

 

I know sean herron is crazy about micro by the name APRIL FOOL, check the gallery or try the forum search function.

 

TS Bob Allen, owned and used by the Sea Cadets in the UK is 42 ft and rigged as a (poleacre) brig. (poleacre = yards come down to deck) No-one needs to climb the mast in these, and if you did it would significantly affect the stability.
See http://www.brig.bob.allen.freeuk.com/

There were naval training vessels usually rigged as brigs (two masts, square-rigged on both) rigged in open clinker 20-25 foot boats.

The Joseph Conrad (ex George Stage) was considered the smallest fully-rigged ship (three masts all square rigged) at 100 ft deck, and 213 tons, see:
http://en.wikipedia.org/wiki/Joseph_Conrad_(ship)

Good luck looking for a design.

 

Not sure what you mean. A ship (of old) has 3 masts or more otherwise she is a Brigantine,Schooner,Ketch or a sloop.

Crows nests can be mounted on just about anything with the stability and suitable roll period, how usable they will be depends onthe overall vessel size you wouldn't generally require to post a lookout in heavy weather, just calmer reef avoiding exploration .