One item on many lists of English usage mistakes is without/with no further adieu for without/with no further ado. I can’t remember that I’ve ever encountered it in real life, like many (maybe most) items on many (maybe most) lists of English usage mistakes. I don’t use either ado or adieu a lot anyway. I also pronounce them differently, with a /j/ (‘y’ sound) in adieu, which I had assumed was the standard pronunciation, but Dictionary.com lists the pronunciation as ‘ado’ first.
I recently encountered “without further due” in a Youtube video. I first thought the high-level English-as-a-second-language speaker said “without further adieu” with the schwas elided, but after listening to it many times, I’m sure he says “due”. This appears in the subtitles, which seem to non-automated, because there is sometimes further explanatory material as well the transcription of the voiceover, there are no auto-subtitling mistakes, and several English-as-a-second-language speaker infelicities. He and I pronounce due with a /j/ sound.
Without further due also appears on some lists of English usage mistakes but I hadn’t seen it before, or encountered it in real life. To me, without further adieu makes sense only in the context of saying goodbye and departing from somewhere, not when introducing a topic. Without further due only just makes sense, if you use due as a noun, which it is in give them their due.
Google Ngrams and a general Google search both show that without/with no further ado is used many times more often than either adieu or due. Many of the first results are dictionaries, usage guides etc, but there are enough instances of adieu and due to say that they are used, mostly in informal contexts.
Ngrams shows that without further ado is 96 times more common than without further adieu, and 522 times more common than without further due. Search shows 35 and 187 times, respectively. (There are obviously discrepancies between how Ngrams and Search use their data, but for general purposes the numbers above are sufficiently similar. The ratios are almost exactly the same.)
In lists of usage mistakes or elsewhere, no-one seems to fulminate against without further adieu or without further due in the way that they do against irregardless, so it may be much adieu about nothing. Speaking of which, much ado about nothing (I used that phrase in my post about irregardless) is either about 10,000 (Ngrams) or 1,485 (Search) times more common than much adieu about nothing. A brief skim of the results for much adieu about nothing shows that it is reasonably likely that people are using it deliberately, as a pun. It is also possible to use without further adieu deliberately …
So adieu
adieu
…