[Siegmund]

I am going to second the suggestion of something in the clockwork department. Perhaps one of the complicated orreries, that gives the time, date, phase of the moon, and position of all the planets.

The optical range and direction finders, combined with mechanical computers to calculate the direction and elevation of the guns, used on WWI-era battleships may also be a candidate. (By WWII these were electrical analog computers, I think, but the early ones, at least, were mechanical...)

In more modern times, the hologram might be a candidate - it requires electricity to create one, but not to view the several images contained in one. If you judge complexity based purely on bits of information contained, rather than number of moving parts, your winner will almost surely be something like holograms or microfilm. The latter may be more to your taste, since it can requires just a mechanical camera and chemicals.