The most common and most likely answer to this crossword clue is the 4 plus 2 plus 3 plus 6 letter word SLIP OF THE TONGUE
I've seen this crossword clue in Financial Times
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More clues leading to the result SLIP OF THE TONGUE
- Uptight oneself, start to object to broadcast mistake one hears
- Wayward word uttered by hopeful setting out to claim love?
- Hit shot up to fine leg? A mistake
- Insolence in smooth and villainous tone, huge error in speech
- Mistake by speaker? Feel tough points should be altered
- Footling upset he passed off as minor mistake
- Verbal gaffe that might make a trainer uncomfortable?
- … in soft enough ground, accepting initially even the error exiting the trap?
- Mouth part commonly straight in singing middle of duet causes vocal error
- Verbal infelicity represented in time with huge note?
Buddy explains!

The straight part
We know that "minor mistake" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case minor mistake = slip of the tongue.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.