The most common and most likely answer to this crossword clue is the 6 letter word LIPOMA
L
I
P
O
M
A
More clues leading to the result LIPOMA
- Doctored mail about cocked-up surgery for tumour
- River interrupting capital growth
- Flintoff to Ponting, perhaps after line “one Australian Fat Lump”
- Endlessly complain, suffering a tumour
- Mail strewn around post office may result in a cosmetic problem
- Starts to prevaricate over man in trouble — flipping fatty lump
Buddy explains!

The straight part
We know that "cosmetic problem" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cosmetic problem = lipoma.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.
Crossword Answer definitions
LIPOMA noun- A nonmalignant tumor comprising fat cells.