To a lot of fans, Pan is to Dragon Ball Z what Willow is to Buffy The Vampire Slayer - she shows up late in the game to whine, get in the way, and occasionally motivate the story by barging into trouble. So, obviously, to some fans, she is endlessly annoying.
When Pan's a kid, she's adorable. No one is arguing that. But just like any cute kid, she grows up into adolescence. That means the next time you see her, she's hot-headed and bratty. That's true to life, reflecting how puberty actually plays to anyone who has passed through it, but that doesn't mean it makes for good anime.
Of course, a lot of people tapped out at the basic fact of the character: She's Goku's granddaughter. If adding a "cute" offspring is a sign of narrative desperation, then surely adding a grandchild is even worse. That's the thinking, anyway.
Speaking of her grandpa, Pan once sassed Goku. What else does a character who doesn't inspire much confidence have to do to grate on your righteous, DBZ-loving nerves?
If you remain unconvinced, this video should do the trick, but be warned - you may never watch the show the same way again.