How frequently do civilian aircraft have mechanical issues to which passengers are oblivious?
I don't think you'll find a definitive answer because most will be just considered routine items, but if you're including non-safety-critical items then I imagine the answer is &quot;lots&quot;. Passenger aircraft are huge, complex, mechanical devices with many many parts. It is accepted and expected that some of these things will occasionally fail.
Most of these can fail gracefully without impacting the flight in any way beyond a note in the tech log. Not only that, but lots of things can be known to have failed but still allow the flight to go ahead as normal.
You may wish to explore the idea of Minimum Equipment Lists. These provide exhaustive lists of items which can fail and flights can still be dispatched as normal. Note this isn't the same as an in-flight failure occurring and continuing to the destination - items in these lists can be failed before you even take off.
For example, here's one for the Airbus A320: https://fsims.faa.gov/wdocs/mmel/a-320%20r21.pdf
Everything listed in that document can be failed in some way, but a flight still operate as normal (with exceptions, as per the remarks column)
For example, and to highlight the level of detail, an Airbus A380 does not need to be grounded because the &quot;PA In Use&quot; notification light doesn't work.