A two-time winner of the ASCAP Pop Award for writing one of the Most Performed Songs of the year, he has had three Billboard Hot 100 Top Ten singles and one #1 Adult Contemporary hit.

Songs he has written have been featured on RIAA-certified gold and platinum records in four consecutive decades: the 1980s, 1990s, 2000s and 2010s; and on the Billboard Top 10 charts for 30 years.

[27][28] Earth, Wind & Fire recorded "You & I", a single Mueller co-wrote with singer Robbie Nevil that was a Billboard R&B Chart Top 30 hit in 1987, reaching #29.

[28] ABBA's Agnetha Faltskog recorded Mueller's "I Wasn't the One (Who Said Goodbye)", which was a Top 20 hit in 1988, reaching #19 on the Billboard Adult Contemporary Chart.

[28] George Benson's "No One Emotion", which Mueller co-wrote with Clif Magness, was released as a single in the UK in 1985 where it reached #76 on the Official British Pop Chart.

Mueller's work in the U.S. has been featured on RIAA-certified platinum and gold records by artists including: Heart, Amy Grant, 'N Sync featuring Justin Timberlake, Lea Michele (on the Glee: The Music, Volume 2 Soundtrack), Jennifer Paige, Earth, Wind & Fire, SWV, Al Jarreau, George Benson, Aaron Carter, El DeBarge, Agnetha Fältskog of ABBA, Peter Cetera, and The Pointer Sisters (on the Billboard #1 We Are The World album).

Internationally, Mueller's songs have been on the UK's BPI-certified platinum and gold records by artists including: Girls Aloud featuring Cheryl Cole, Eternal, Steps and Australia's ARIA-certified gold records including: Jennifer Paige, Lea Michele (Glee: The Music, Volume 2) and lead singer of Little River Band John Farnham's solo album Age of Reason, which went 11 x platinum.

"[38][39] In September 2018 Carrie Underwood sang a brief, spontaneous duet of the DuckTales theme with Jimmy Fallon after telling him it was one of her young son's favorite songs.

[42] For the NBC-TV musical comedy series Rags to Riches, Mueller wrote new comedic lyrics for existing hit songs from the '50s and '60s that were featured in most episodes of both seasons of the show.

With Lalo Schifrin, Mueller co-wrote all songs featured in the original film musical Berlin Blues, starring Julia Migenes.

Mueller's songs have been featured in films including: One Hour Photo, Pokémon: The First Movie, Money Talks, B*A*P*S, National Lampoon's Vegas Vacation, The Last Starfighter, Adventures in Babysitting, Simply Irresistible, The Legend of Billie Jean and Honey, I Blew Up The Kid.

[36] Mueller wrote the lyrics and co-wrote the book of an original musical titled Butterfly, which was directed by Jack Hofsiss and performed at the Goodspeed Opera House.

Mueller also created an original musical, How The Hell Did I Get Here?, with Downton Abbey star and SAG Award-winning actress Lesley Nicol.