It'd be slightly more limited than a standard Tamagotchi, but not by too much. And it'd be nifty.
Firstly, pixels would be out. (Mechanical pixels by flipping discs is possible, but not suitable for this application.) They could probably be replaced by clear plastic scrolls with the characters on them. Of course, this might limit (or even eliminate) branching when it changes, but oh well. One scroll for the characters (both reels mounted to something to move it up and down a bit for movement), one scroll for that skull thing, one for when it takes a dump, and a nontinted to tinted outmost one for day/night (lights?). And of course a fixed background, similar to a normal tamagotchi.
Instead of 3 buttons (next/select/cancel), you'd have one button (possibly a shaft pusging a lever where the hinge end is like a gear) for each icon. Of course, some things would need simplified, either 1 type of food/snack, or more likely one button for food and one for snack.
Stats could be stored with mechanical counters similar to the trip-odometer in a car - with counters for things like 'weight' or 'happy' shown through the front (no need for a stat-icon button then either), counters for internal variables (like length of time sick, etc) kept back in the insides somewhere.
The timing 'pulse' for things like time between mess and sick left, time between sick and deal left, etc. would probably be from a gear with a pin on it geared up/down to 60rpm or 1rpm, powered by the main motor (more motor details later), where the pin strikes something to increment the counter. Of course, things like 'wash' and 'meds' would reset the counter and disengage the pulses.
day'night probably controled by some sort of clock setup similar to timer-outlet things (the ones with the mechanical detents for stop/stert), although an odometer-style clock would be shown on front.
The few non-purely-mechanical parts, of course would be the motor and associated power stuff. Most likely a synchronous motor, and a transformer for 220 mode (modes selected via a dpdt knife switch in back). There'd be a 'master gear' selector to compensate for 50/60Hz timing differences. all other machine-altered mechanicals (odometer-style 24-hr clock, mess/ill counters, scrolling, character up/down, etc.)
Of course, not sure whether it'd be better to build it to a metal frame to show off the guts, or to build it in a Plexiglass (no corner joints, rounded or glass (with corner joints) enclosure is an interesting thought. Perhaps a Bakelite base?
Any questions, complaints, thoughts, or (related) rants? Feel free to post a comment.