A digital signal works most of the time but occasionally reads wrong. Which instrument, and why?

An oscilloscope, because intermittent "digital" failures are usually analog/signal-integrity problems that a logic analyzer can't reveal. A logic analyzer only reports whether each line is above or below a threshold, so a signal that's marginal, a slow or rounded rising edge that crosses the threshold late, a "high" that only reaches a borderline voltage, ringing or overshoot that causes a double-clock, ground bounce, or a runt glitch, looks like a clean 1 or 0 on the LA and gives no hint of the real problem; in fact the LA might even sample it as correct most of the time, matching the intermittent symptom. A scope shows the actual waveform, so you can see the edge is too slow (the weak-pull-up I²C case), the level is marginal, there's ringing causing extra transitions, or noise is corrupting the signal near the threshold, the electrical root cause the LA masks. You'd set the scope to trigger on the suspected condition (and possibly a glitch trigger) to catch the bad event, measure rise time and voltage levels against the device's logic thresholds, and check the signal at both the driver and receiver ends. The general principle: when a signal misbehaves intermittently and "the logic looks right," suspect the physical layer and put a scope on it, because the bit may not be a clean level even though it usually reads correctly. The LA tells you the logic is occasionally wrong; the scope tells you the edge/level is the reason.