Pssst! No one tell Gargoyle that most/all of these are already existing palindromes. Behold…the power of Google.
Doc, note: I dissent. A fast never prevents a fatness. I diet on cod!
God, Rey, G. – Ni! N… Rub? I burning yer dog.
I have to admit, this is makes more gramatical sense than Thaidog’s original post.
I beg your pardon – two of mine (and, clearly, several of the others) are entirely original.
Mine are original. Sup pus. 
Ma, I…redder I am.
(It just kills me that I can’t invent a better palindrome to apologize. Kills me. You know that, don’t you?)
Mod, enema, assuage, gauss, AA, men, Edom.*
Now to parse it…
Mod enema, assuage Gauss; AA men, Edom!
Y’know, “Moab is my wash-pot; over Edom will I cast out my shoe”. That Edom.
Best dirty Palindrome ever written:
No, son, Onanism’s a gross orgasm sin: a no-no, son.
A Glaswegian sends an SMS message to a Catholic priest, Father Tom, who has an illegitimate daughter named Kate, and is threatening to reveal her parentage, while making a pun on the word “father”.
The following exchange records the message, and his reply:
“Re. K: c u Fr. - eh Tom?”
“Motherfucker.”
(God that was tortuous.)
Thank you for making my day!
Unremarkable was I ere I saw Elba, Kramer, nu?
(Not mine, but a lovely confession nonetheless.)
Aim at OP o’ semen, Ygor: DNA androgyne Mesopotamia.
Mine wasn’t good, but I think it is original.
Drink cus u suck, nird!
Doc Note: I dissent. A fast never prevents a fatness. I diet on cod.
Borrow or rob? Yes
Aw, oi, Goy Og, Iowa.
or
Ohio, goy Og, oi! Ho.
Name a demand! Esa reign! I don’t ask. Come here he mocks at noding. I erase DNA. Me Daeman.
Hey! Yo has tits ahoy! yeh?
Since we’ve abandoned all pretense of limiting ourselves to insults, I’ll just post one I’m proud of, based on Poussin’s Shepherds of Arcadia:
In Eden, I? Never! Even in Eden, I.