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.
Some hardcore Dragon Ball Z fans have denounced Kai as dishonoring the original series by removing much of the character inherent in the extended stories, while others enjoy the much faster-paced plot.
Many fans who grew up watching FUNimation's original Dragon Ball Z dub decry Kai's change of dialogue (even though Kai's dubbed English scripts are far more accurate), the changes in voices (even though Kai benefited from Sabat, Schemmel, and others gaining a decade of voice acting experience since the original dub), and the loss of Bruce Faulconer's music (which was disliked by fans of the original Japanese version of Dragon Ball Z back in the day).
All of above is taken Up to Eleven with the Latin American viewers. Unlike North America, we only have one dub, and it was perfect. After Kai shows up, well...
For most English speakers in North American part of the hostility comes from losing many beloved voice actors, such as kid Gohan, Bulma, and Android 18. Not helped that the person who did kid Gohan constantly played Gohan since Funimation took over up until Kai. Also, the original dub of Dragon Ball Z did moved closer to the original script by the middle of the Android Saga (with the Buu Sage being the most faithful) and many of the new lines from Kai's Saiyan Saga up to the middle of the Ginyu arc are quite similar to Dragon Ball Z uncut. So, the added benefits of having a more faithful dub is only really gained for the last half of the Ginyu fight up to the beginning of the Android Saga. With that said, most still enjoy Kai as its own thing and do enjoy the new music along with the stronger vocal performance from the veteran actors.
Narm: Sure, Gohan's screams are properly full of emotion... but some of them carry on so long that it loses the intended effect.
Narm Charm: The Ginyu Force's entrance. No matter what language it's in, the poses and song that accompanies them so completely cheesy that it can't help but be entertaining.
Superlative Dubbing: The English dub is close to flawless, since most of the voice actors have been voicing these characters for over a decade.
Suspiciously Similar Song: This ended up being so widespread in composer Kenji Yamamoto's work that Toei Animation actually kicked him off the show towards the end of its run, and the music for the series, except for the eyecatch and opening/closing themes, was replaced with the original Japanese DBZ soundtrack. The English dub followed suit starting with episode 64 and all reruns of episodes previous to this. The DVD releases were also affected beginning with the fifth DVD set.
It should be noted that Yamamoto was doing this as far back as his days working on DBZ: the insert-song "Battle Point Unlimited" (used in episode 120, when Trunks goes Super Saiyan and kills Freeza) is a pastiche of an entire album (1985's A Secret Wish) by the German synth-pop band Propaganda
Woolseyism: The first half of the English Kai dub scripts were adapted faithfully yet cleverly by J. Michael Tatum, and it's almost always mentioned as a plus when discussing the dub. The second half lacked his involvement and it shows.