My first and obvious thought was that the interrupt flag (realized by a
74HC74) was defective. Since I didn't have a 74HC74 at hand I used a 74HCT74
as replacement - and the FZ-1 seemed to work again. However, stress testing
showed, that the problem showed up only less often but was still present. It
looked like the clear signal generation was causing the problem.
I grabbed a multimeter and checked it. Indeed, the reset signal showed up
all kinds of weirdnesses such as overshoot, undershoot and - even worse -
spikes and breakdowns. Having a look at the schematics I realized that
the address multiplexer (74HC154) was the part responsible for this signal.
After replacing it with a 74HCT154 everything was fine again.
Casio obviously seems to love hide-and-seek games and thus didn't use
usual part numbering, so here are the positions of the two mentioned ICs:
Location of 74HC74 and 74HC154