the difficult or unpleasant part of a task or situation – informal
2000 - Sunday Times : Johannesburg - I still feel a bit sorry for Hugh, he always seems to get the dirty end of the stick.
dirty work at the crossroads
illicit or underhand dealing – humorous
This expression is recorded from the early 20th century and may reflect the fact that crossroads, the traditional burial site for people who had committed suicide, were j once viewed as sinister places.
1914 - P. G. Wodehouse - The Man Upstairs – A conviction began to steal over him that some game was afoot which he did not understand, that - in a word - there was dirty work at the crossroads.
do the dirty on someone
cheat or betray someone - British informal
get your hands dirty = get dirty your hands
do manual, menial or other hard work
become directly involved in dishonest or dishonorable activity – informal
1998 - Spectator - Unlike its sister churches in the West, the Catholic Church in the Philippines is not afraid to get its hands dirty.
speak about sex in a way considered to be coarse or obscene – informal
wash your dirty linen in public
discuss or argue about your personal affairs in public
This expression dates from the early 19th century in English.
A similar French expression about linge sale is attributed to Napoleon.