"quite incidentally" is a perfectly acceptable phrase to use in written English.
It means "by the way" or "unexpectedly". For example: "He happened to mention, quite incidentally, that he was selling his car."
Williams' homer had, quite incidentally, made the score 4 3.
Does etiquette require that we conform to the information we acquired late, and quite incidentally?
In this time he quite incidentally formed much of my musical tastes, and they have lasted a lifetime.
Both rooms are used to study sound effects, and, quite incidentally, to send visitors home happy with the idea that they understand science.
These concepts need to be reintroduced regularly – and perhaps indefinitely – for full effectiveness, a lesson I learned quite incidentally one horrific day.
And, quite incidentally, one may feel pleasure that so excellent and modest a young actor as Harrison Ford has been progressing so steadily all these years while hosts of patent-leather haired leading men have come and gone.
In 2003, Savage said that he voted in 2000 for George W. Bush "quite reluctantly, incidentally".
We calculate that we can create monuments on the same scale as Arizona (it's quite beautiful, incidentally) at every State Capitol in America for roughly the same amount of money that is would cost to build the Vietnam Veterans Memorial in Washington today--in the neighborhood of $24 million.
(To depict a boring person as such, without being boring, was, incidentally, quite difficult).
There is, incidentally, quite a breast implant theme emerging in this series: Caroline's grotesque spouse was going to buy her a boob job for her birthday in the last episode.
They were also, incidentally, quite merciless toward the shibboleths that Deresiewicz implicitly accuses them of propagating: don't split infinitives, don't end a sentence with a preposition, and so on.
