Nick. Either an OK Red who has issues with confronting problems (Namely, fans criticize that Nick runs away from all of his problems and frequently gives up), or an unlikable "chosen one" character who gets undue focus at the expense of the other Rangers.
Koragg. Either a legitimately interesting villain, a Token Good Teammate, or a poor man's Villamax, whose honor does not work as he works with evil forces with no shades of grey?
While Xander is still one of the most popular characters in the season, several fans have pointed out how he has Aesop Amnesia (In that he learns three times to stop being an arrogant jerk, but it never catches on)l
Broken Base: The theme song which people either find it to be okay, or hate the hip-hop like direction it took.
Complete Monster: The Master, whose real name is Octomus, is a demonic entity intent on destroying everything good. Prior to the start of the series he brainwashed Leanbow into becoming his loyal servant Koragg. Once he emerges, he possesses a follower who had turned good and was trying to prevent his rebirth and mutates his body into his own twisted image; he then possesses Leanbow's son Nick directly, transforming him into a much more sadistic and vicious version of Koragg who laid waste to parts of the forest and Rootcore before he was saved. After being exorcised from Nick, he attacks and destroys the Mystic Mother's palace in a matter of minutes and kills both Leanbow and Daggeron when they investigate the destruction before dropping their corpses down before the Rangers; finally he obliterates time itself, transporting the rangers to the future he plans to create where he's reduced the Earth to a barren, lifeless husk for no apparent reason other than because he can.
Creator's Pet: Nick is seen by some as being this. The final episode takes steps to remove him of this status though, by having him give up instead of trying to fight The Master. Although it quickly steps away of removing him from this when the other rangers say he's their only hope and has "always been the one to hold them together", despite alot of evidence to the contrary.
Crossover Ship: While not a romantic one, Chip and Dustin from Ninja Storm are commonly best friends in fandom due to being the nerd of their teams and for being the only male yellow Rangers (Which is commonly lampshaded during fanfics).
Xander, maybe it's the accent, maybe it's the wannabe Loveable Rogue vibe his smarminess gives off, maybe it's just the color green. When Operation Overdrive had a multi-season team-up episode instead of a full two-team crossover, Xander was the one brought in from Mystic Force. He's so much this that they had another Green Ranger get a promotion to Red Ranger.
Chip, while less popular, still has a notable fanbase, primarily due to being one of the few yellow Western Rangers who's a guy (Super Sentai have plenty of yellow males before, but Saban commonly adapt them to women for gender balancing purpose). His boundless enthusiasm, particularly at getting the chance to become a Power Ranger, is also a notable characteristic that helps him stand out from others in the series.
The trio of Claire, Leelee and Phineas, particularly due to their team-up in "Light Source". Linkara even noted that they had more effective Character Development than the majority of the Rangers themselves.
Genius Bonus: The Manticore Megazord is based on a obscure mythological beast with the body of a lion, a human face, bat wings, and a scorpion tail. The Megazord is lion-based for the most part, but cheating with being part-firebird, has a human-like face like all megazords, grows wings of fire before using it's finishing move, but no tail.
Although this series was the second that was a joint production between Toei and Disney (the first being it's source material), it was frequently compared to Harry Potter, which is not a Disney property. Six years later, Toei wound up releasing a Sentai whose theme was comparable to a Disney property...Pirates of the Caribbean
It's the Same, Now It Sucks: A large amount of complaints about this series is just how similar it is to Magiranger. While it's not as much of a direct copy as, oh say, Samurai or Wild Force, there's a lot of elements that make it hard to not view it as essentially a dub of Magiranger - for starters, this was the first series since Zeo not to change the villains (previous seasons had either changed details, added an original villain, or removed an antagonist), the family subplot, while not present from the start, was still there, and was much more obvious, and much like with it's source material, the red has a lot of focus.
If Disney gave them 38 episodes instead of 32, we would have gotten a proper introduction to the Mystic Mother (and maybe explain how Rita had gotten that position), who only showed up in the 2-part finale.
Unintentionally Unsympathetic: Nick. The gist of what happens to him: He was separated from his parents as a baby, drifting through random relatives in his adopted family, never had time to settle down and make friends, discovers his mother was the sorceress who mentored him in magic, learned his archenemy is his brainwashed father, and discovers it's his destiny to defeat the Master of the Underworld. If it were any other Red Ranger, this would work. Unfortunately, Nick is very unfriendly, brooding and is usually the first to just give up when things start to fall apart, and yet he's supposed to be the glue that holds the Rangers together. His cold response to Leelee, who was trying to reform, was so cruel that even the other Rangers, who didn't even like her, felt he went too far.