Keep in mind that there are different ways an OC-related issue can show up.
When your CPU makes a mistake, there is some chance you notice - for example, due to a program crashing, or visual artifacts in a game - but there is also a chance that you don't notice. There are different errors a CPU can make that have different results.
One error that would not cause any problems is a mistake in a branch prediction. Since the CPU knows that the branch predictor is often wrong, it checks the predictions and recovers if the predictions are wrong. Since the branch predictor doesn't affect correctness, the worst case result would be a tiny slowdown. Another error that wouldn't matter is an error that corrupts information that isn't reused. Every time the CPU adds two numbers, it tracks some "flags" that note if the result is positive, negative, or zero. If a flag is miscalculated - but isn't checked - nothing bad happens.
An error that would cause a crash might be a mistake in a TLB, or a mistake reading / decoding an instruction (which could result in the CPU trying to do something illegal). Depending on what code happens to be running when this happens, the result could be a single application crashing or the whole machine crashing.
An error that could silently corrupt data would be a bit flipping in a floating point calculation. If, say, you're doing your taxes and your CPU is overclocked, it's possible that one of the bits of a floating point calculation doesn't get back into the register file before the clock ticks, so the wrong answer is stored. You might not notice so long as the error doesn't cause an obvious discrepancy... that's silent data corruption. Another example would be a media encoding app that sometimes corrupts video frames. You won't notice until you try to watch the video later.
Given a flaky CPU (which intermittently makes a specific type of mistake, e.g. calculating an incorrect multiplication), it's very possible for some applications to crash horribly (e.g. assuming that a multiplication result won't be zero, and dividing by the result of the multiplication) and for another application to appear to work, but produce subtly incorrect results. If there is any test that fails with a certain OC, it's risky (at best!) to consider that OC "stable for other tasks".
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