What could "mucka doozy" mean and where does it come from?

I have heard a similar phrase in Scotland. Someone is "muckle dozy" if the are very stupid or slow-witted. This seems to fit the circumstances of your question, where light-hearted insult might be applied to someone who did not learn quickly enough.

muckle = >also mickle [mikl], arch. meikle [mikl]

adv. Qualifying a v.: much, to a great degree or extent, greatly

adv. etc. in the positive or comparative degree: much, greatly, very, exceedingly

Scots online dictionary

dozy = UK informal "thinking or reacting slowly"

Cambridge Dictionary

To add to my answer, I note that many immigrants to the east coast of America were from Scotland. They would have brought their language and vocabulary with them, including the word "muckle", which goes back to the 1700s or before as in the Dictionary of the Scots Language (DSL) below. It is therefore likely that the word would be used to qualify the linguistically more widespread "dozy".

I restrict myself to merely three of the many early DSL examples:

Muckle = Of quantity or degree: much, a great deal of, a lot of (Sc. 1808 Jam.).

“Contrair to just Rights and Laws I've suffer'd muckle Wrang.” Abd. 1768 A. ROSS Helenore (S.T.S.) 64:

“Yes, yes, twa men I saw, ayont yon brae,” She trembling said; “I wis them muckle wae. ”Edb. 1773 FERGUSSON Poems (S.T.S.) H. 193:

They are fear'd for denial o' quarter to themsells, having dune sae muckle mischief through the country.s.Sc. 1859 Bards of Border (Watson) 8:

[Scots Language Dictionary](Dictionary ](https://www.dsl.ac.uk/entry/snd/muckle)

You may like the recent use of muckle in:

"PM branded a ‘muckle glaikit numpty’ as SNP conference debates Scots language"

London Economic

(I Leave the definition of "glaikit" as "an exercise for the student")

I cannot see why a Scottish adjective (muckle) would be paired with an English word (dozy) that is not used as a noun.

... this phrase, "mucka doozy". I always understood it to be a 'big mess' or something to that effect.

I suggest that what you heard was "mucky doozy" = a really filthy mess; a horrible mess, etc.

OED:

Mucky = 1.a. Covered with dirt or excrement; dirty, filthy, muddy; involving dirt or filth.

1937 ‘G. Orwell’ Road to Wigan Pier ii. 26 It is bad going underfoot—thick dust or jagged chunks of shale, and in some mines where there is water it is as mucky as a farmyard.

OED:

doozy, adj. and n.

Etymology: Of uncertain origin: perhaps variant of daisy

slang (originally and chiefly North American).

A. adj. Remarkable, excellent; also, amazing, incredible.

1903 A. Kleberg Slang Fables from Afar 83 As soon as the races were billed he began to evolve schemes—one doozy scheme followed the other.

and, hence, the noun - note the reference to irony:

B. n. Something remarkable, amazing, or unbelievable. Frequently ironic.

1916 Dial. Notes 4 274 Dozy, term of praise. ‘Isn't that fish a dozy?’

1959 ‘R. Macdonald’ Galton Case vii. 53 I married him—the big mistake of my life, and I've made some doozies.

It seems likely, if you've not heard the phrase from anyone since your old manager, that it was part of this person's personal idiolect.

As such the rest of us can only speculate on what it might have been. My own supposition is that what you were hearing was, or was derived from 'much ado', or possibly in the plural, 'much ados'.

'Ado' simply means (per Chamber's dictionary) 'a to-do, bustle, trouble, difficulty, stir or fuss'.

The word is not widely used outside of the phrases 'without further ado' and 'much ado about nothing'.

'Much Ado about Nothing' is the title if one of Shakespeare's plays. In this context 'nothing' means gossip or things overheard, but generally when people use the phrase 'much ado about nothing' they mean 'a lot of fuss over nothing much'. 'Much ado' always has the approximate meaning of a 'big fuss'.

The second word is probably doozie. It's an American dialectical noun meaning something that is much greater or bigger (in any sense) than most others of its kind. And it's often used in a negative way (e.g., "that's a doozie of a mess you've gotten yourself into.")

The whole phrase might be muckle doozie. Mickle, or muckle, is a Scottish word meaning huge, so adding the word muckle just intensifies the word doozie.

The word muckle seems to be generally limited to Scotland, but there are lots of Americans with Scottish ancestry, so it wouldn't be too surprising to hear it used in the U.S., especially in a fixed expression like this.