MIKE&TRICIA'S HOLLYWOOD DIRT REPORT

MARIAH CAREY MURDERED HER SONG AT THE ROCKEFELLER CENTER TREE LIGHTING: MARIAH CAREY sang "All I Want for Christmas Is You" at last night's Christmas tree lighting in New York City ... and by some accounts, butchered the hell out of it.

Mariah was supposed to have taped the performance Tuesday night, but NBC execs called it off after she left everyone waiting for three hours. TMZ says it was because she was busy talking to her divorce attorney, while E! Online claims she didn't want to perform because it was raining. Either way, the decision to cut her from the show was made.

She was later able to somehow work it out and Mariah was allowed back on, but because there was no longer any time to pre-tape her performance, she was forced to sing live. And that didn't go so well.

Carey missed most of the high notes she's famous for, leaving her backup singers to pick up the slack. Here's what Mariah sounded like on TV last night, with the band and the backup singers behind her ...



And here are the isolated recordings of her vocals at the beginning and end of the song that were online within hours of the broadcast for comparison's sake. (CLIP 1) (CLIP 2)

RELATIONSHIP REPORT: JOHNNY DEPP and Amber Heard have decided to take things slow, following their whirlwind romance and sudden engagement. That according to a longtime friend of Depp, who tells People magazine, "There is no rush to marry at the moment," adding, "Johnny is crazy in love with Amber, but there is turmoil in the relationship."

One of the problems reportedly stems from their age difference. Heard is 28 -- 23 years younger than Depp -- and has developed a reputation as a free spirit. Claims the source,"Amber flirts and has many different kinds of relationships. She is not really ready to settle down."

2. New couple alert! Word on the set of the show "Madam Secretary" is that TEA LEONI is dating co-star TIM DALY, who plays her husband on the show. "Their chemistry on set is electrifying," a source tells Us Weekly, adding Leoni, 48, and Daly, 58, "have an amazing time filming."

Last month the pair was spotted walking down a street in Los Angeles "with their arms wrapped around each other," according to a Us Weekly source, adding, "They were definitely couple-y."

Leoni divorced DAVID DUCHOVNY this past summer after 14 years of marriage.

BABY POOP: SHAKIRA's baby bump is pretty huge. The Colombian cutie is about 7 months pregnant. (PHOTO)

Word is she and her soccer stud partner, who already have a 1-year-old son together, are expecting another boy.

2. "Tonight Show" host JIMMY FALLON and his wife welcomed a baby girl yesterday. "Frances Cole Fallon officially entered the world at 8:45 a.m. on December 3, weighing 5 lbs., 11 ounces and is 18.5 inches long," a rep for the couple told People magazine.

Frances is the couple's second child. Both Fallon babies were born via surrogate.