The most common and most likely answer to this crossword clue is the 10 letter word LEAFLETTED
I've seen this crossword clue in Financial Times
L
E
A
F
L
E
T
T
E
D
Buddy explains!
The straight part
We know that "having distributed flyers (some say incorrectly)" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case having distributed flyers (some say incorrectly) = leafletted.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.