The most common and most likely answer to this crossword clue is the 8 letter word FLYSPECK
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Buddy explains!
The straight part
We know that "Pest's dropping" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case pest's dropping = flyspeck.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.
What does FLYSPECK mean?
FLYSPECK noun- Housefly excrement, visible as a minuscule black dot.
- (by extension) Anything tiny or insignificant.
- To bespeckle with tiny spatters of color.
- To inspect in minute detail to ensure that something contains no flaws; nitpick.