These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Walter: (reading question) "Dear Walter, why do I gag when I brush my tongue but not when I give my boyfriend oral sex?" (to the girl who asked the question) Well obviously, your toothbrush is bigger.
Likewise, Peanut's story about ordering food from a Chinese restaurant is so offensive that it becomes purely hilarious. (And in case you didn't catch it, Peanut will remind you several times!!) It gets even funnier when Jeff tries to get Peanut to apologize for the joke and read a letter from an Asian fan.
There was a bit at a live show in Winnipeg where Peanut finds the idea of a vomiting giraffe hilarious.
At one show, there was no roof and an airport nearby. Achmed was on stage...
Mexicans Love Speedy Gonzales: According to Arab-American comic Ahmed Ahmed, goofy acts like Achmed the Dead Terrorist are actually a big hit in the Middle East. Fellow comedian Gabriel Iglesias would later back this up even further when, during his Aloha Fluffy special, he tells of when he went to perform in Saudi Arabia and is told by a cab driver that Jeff Dunham is considered the #1 most popular comedian in the area.
Older Than They Think: Jeff's been doing ventriloquism his whole life - started in elementary school (fourth grade), high school, college and on. He's done local commercials in Texas, and bits for churches, groups and corporates. When he was in college he toured nationally with the Broadway variety hit Sugar Babies in 1984-1985. The only character he had from then he still uses is Jose Jalapeno, but many people have had a moment of "Wait, I remember this guy!" when he pulled Jose out.
Pandering to the Base: Dunham has been doing this in recent years by featuring Achmed more often and doing more humor to appeal to Southern conservatives.
The Scrappy: Sweet Daddy D. Aside from all the Unfortunate Implications involved with his character, he wasn't really that funny, and his cut-aways during Walter's part of the special were more annoying than entertaining. It's probably a good thing that he hasn't appeared in any of Jeff's specials since.
Special Effects Failure / Throw It In: This happens a lot with Achmed, as his skeletal body is unusually flimsy compared to the rest of the puppets. During a few of his specials, Achmed's entire lower body will have to be repositioned, much to Achmed's chagrin (including one incident where he reacted in horror when Jeff accidentally pulled his arm off). To Jeff's credit, he rolled with the incident, making up a story about how his pet chihuahua used Achmed's dislocated arm as a chew toy.
One show at Penn State saw Achmed's ribcage getting caught on his spine, starting off 40 minutes of hilarious improv. The same thing happened during Controlled Chaos (the uncut DVD performance), but Jeff actually pulled Achmed's ribcage off trying to get it unstuck.
During Spark Of Insanity, Melvin whipped his body around too fast, and his entire head of hair came flying off. Granted, everyone else thought it was funny, but Melvin wasn't really thrilled ("I look like Lex Luthor!"). This also happened to Peanut in Arguing With Myself and he wasn't happy about it, because it hurts trying to stick it back on.
The DVD extras reveal that that one was planned from the get-go.
The Achmed arm thing from the Christmas special was also planned. This troper saw that same gag the January before the Christmas special came out (they filmed the DVD in July or so), almost word for word in the Billings, MT appearance. It may have been a mistake at first, and the audience response was so good that he kept it. Though he also truly did throw in a very well-received Montana joke.
Walter: So where are we again? Jeff: Billings. Walter: Montana? Is this the entire population of the state? Audience: *HUGE applause*
Though Jeff is quite good on keeping his lips still with the other puppets, sometimes he slips up. In particular, his skits with Peanut have them bantering back and forth too quickly and he can't always keep up.
In a more general sense if you look closely you can see Jeff's adam's apple bouncing up and down when he talks.
Tear Jerker: One moment in his biography, All By My Selves, has him telling a story of how one of his daughters put a suitcase with two dolls and her blanket beside his luggage, and he had to take the suitcase back to her room and tell her she couldn't go, and she was crying as he was leaving and Jeff himself started, too.
Uncanny Valley: Zig-Zagged. Many of Jeff's earlier puppets, especially if you see his school pictures, are more realistic and as a result look incredibly weird. Thankfully the ones he has now are stylized and he's good enough moving them that they don't make any strange movements that are often associated with ventriloquist dummies.
However, Achmed Junior falls head-first into the valley.