Dear World, There Is No 'Z' In 'Muslim'
It's pronounced like it's spelled.
Not to pick on Jimmy Kimmel in particular; it's pretty much a nationwide epidemic.
Comedy Central / Via giphy.com
Just to point out the difference, here's the side-by-side in Roman script.

Ahmed Akbar for BuzzFeed
Most people say it like the right, but it's spelled and pronounced like the left.
And here it is in Arabic script.

Ahmed Akbar for BuzzFeed
Again, same thing. On the right, how it's accurately spelled and pronounced - 'Muslim.' On the left, a COMPLETELY DIFFERENT WORD.
Both languages are in complete agreement there is a difference between the letter "S" and a "Z" in spelling AND pronunciation.

http://giphy.com/gifs/abc-letters-screensavers-11wA1XcOy49M4g

http://www.gifmania.co.uk/Animated-Letters-Animated-Gifs/Animated-Animal-Letters/Alphabet-Frogs/Frogs-Alphabet/frog-z-letter-14354.gif
So where y'all finding the Z?
Via giphy.com
Seriously, where?

NBC
W H E R E

Afp / AFP / Getty Images
H O W

Via imgur.com
So let's say you're like "Nah, I'm good. I'll keep pronouncing it 'Mozlem.'" Here is a list of proposed spelling changes.
Muzlim
Izlam
Benito Muzzolini
Muzcles
Muzzels (like the shellfish)
Muzic
Muzket
Bernie Zanders
Wis Khalifa
Jay-S (the rapper)
Wisard of Os
Mussle (like for a dog)
Taylor Zwift
Pepperoni Pissa ("Let's go get some 'Sa, bro.")
Pazta Sauce
Zpelling Bee
Zalami
Zpaghetti-O's