I asked John Walker who maintains a lovely web site of information about the Analytical Engine whether he knew of any serious attempt to build it. He was kind enough to reply.
To my knowledge, nobody has made a serious attempt to build the Analytical Engine or even a seriously scaled down version of it. I think the general consensus (which, in part, informed the various British commissions which decided not to fund the project) is that it is unlikely in the extreme that a machine which would be necessarily so large would not fall victim to "tolerance creep", where tolerances in individual components would eventually add to make large scale interfaces (for example, between the Mill and the Store) unreliable.
Babbage was aware of this problem and addressed it in his papers. His solution was to design the machinery so that it would jam in case of error, but then the question is, how often would it jam? If it jammed every second and a typical computation took several hours, a room full of people with log tables could out-compute the Analytical Engine.
I'd think it would be beyond crazy to try to raise the funds to construct the complete Analytical Engine. After the Singularity, when we're all 10^16 times as wealthy as at present and can build diamonoid machinery with atomic precision, I'd say go for it, but then tens of thousands of people will have done so within the first 24 hours after the Transition.
Gen. Henry P. Babbage's description of an attempt to build just a component of the Engine:
is instructive of the problems of mechanical tolerances. We can build things much more precisely than in his day (although much of the progress in our technology has been in coping with sloppiness, not improving precision), but ultimately large scale computation depends upon robust digital storage which is immune to noise:
Any macroscopic mechanical system has at best a modest level of noise immunity, and when you imagine a machine the size of an auditorium with hundreds of thousands of parts, the challenge seems overwhelming.
I'm a balding engineer, and I've seen many great ideas founder on the rocky shore of reality. I think the British were *right* not to fund the Analytical Engine; it was a superb idea a century before its time.
So go prove me wrong.
(And ask yourself, as I often do, "What are the superb ideas we have today which are a century before their time?")
I shall continue to investigate. If you care about this topic you can follow the label babbage. If you have an informed technical opinion on this please contact me.