Looks to me like current for the 7 LEDs is sourced out of Q906, which is turned on at the specific time by Q908, which is ultimately fired by U907. The LED current is then sinked back to the controller chip on the same lines that are used to control the numerical digits. So if, for instance, Q906 is not shutting off, but actually passing a small amount of current all the time, then the LEDs will fire every time one of the shared digit control lines is fired. That would account for the flickering of the non-used LEDs. If the transistor then is turned on to full current for the proper LED, that LED will light normally. Just a thought.
This sure does sound like a plausible reason. I investigated, tested Q906 and Q908, found they were operating OK, replaced them anyways and the problem remained unchanged. Then I replaced all the LED segment driver transistors (Q900, Q902, and Q904), but no change.
The only other components I see in that part of the circuit are the resistors, one capacitor C907 inductor L901. Would failure in any of those bleed some current through to all of the units LED segments? Or is the IC a more-likely culprit?
There is a rattle coming from this board every time I flip it over. I've looked carefully at it from every angle and I don't see anything loose that would be causing a rattling noise. The only component that might have insides, as far as I can tell, is the crystal Y900. Is it possible for a crystal to come loose inside its can and rattle around? I was thinking the flickering could be caused by a too-high sampling rate or display refresh rate. The crystal manages that, doesn't it? Still wouldn't explain all the other units LED segment glowing dimly, but....