Once Reiko Yoshida left the Tokyo Mew Mew project, Mia Ikumi tried to write a sequel incorporating the retcons made in the TV show and replacing Ichigo with a new character named Berii. Ichigo herself lost her powers except as a living accessory to the new heroine, her origins and family life were completely ignored in favor of sending her to Europe, and she became a washed-up hero. It's no surprise Tokyo Mew Mew a la mode has a high degree of Fanon Discontinuity amongst fans who also really dislike Berii. Berii herself has been Mis-blamed, though; the real blame lies in the publishers, who, among other things, restricted the series to just two volumes when commissioning the sequel.
For some portion of the fanbase, Magical Record Lyrical Nanoha FORCE has become this for the main continuity of the franchise. The series became Darker and Edgier, but the method of doing so was introducing an Anti-Magic virus into a magical setting. This led the new villains to become a Villain Sue gang that beat beloved favorites almost insultingly easily while being insufferable, hypocriticaljerkasses, the heroes have to combat them with Flawed Prototype weapons that barely even work and the new main character is, unusually, a heterosexual male that has so far not done anything beneficial for the heroes. Even worse, it has undergone a massive Schedule Slip, releasing only 30 chapters in the four years of its publishing. Perhaps due to all of these reasons, it is currently on a possibly permanent hiatus.
A sizeable portion of the fanbase felt that Bleach went into a Dork Age with the Fullbringer Arc. The arc focused on new characters with totally new powers instead of the established characters and featured a plot that seemed almost completely unrelated to any part of the Myth Arc. To be fair, with Ichigo depowered and Aizen alive but imprisoned, there weren't many plot threads that could be carried over directly from the previous arc and at least nothing involved Aizen.
There are also fans who consider the four year long Arrancar Arc a Dork Age. In general, the writing became a lot more divisive after the Soul Society arc, and the series' sales and ratings dropped to the point where the anime was cancelled as soon as the Fullbringer Arc wrapped up.
Anime and Manga in general in The New Tens seems to have hit this for a lot of Western fans. While Moe series are fairly popular in the West, they have a loud and vocal Hatedom who sees them as nothing more than Otakupandering. Of course, Moe is EXTREMELY popular among Japanese otaku, who buy most of the figures, DVDs and such. As a result, series that focus on four highschool girls (popularized by the works of Kyo Ani, especially K-On!) have overtaken the airwaves, while more unique series are becoming rarer and rarer.
Some renowned studios have also taken big hits. Even Studio Gainax has lost some key creators like HiroyukiImaishi and Hideaki Anno, who have formed their own studios. As a result, Gainax seems to have decayed from producing acclaimed original series to mediocre adaptations of Shōnen manga such as Medaka Box. Worse still is that the venerable Studio Ghibli may be edging close to shutting its doors, although a shut down was at least delayed by the modest success of Arrietty.
While still held in extremely high regard by the western anime/manga community for its incredibly masterful art and nuanced characterization, some fans feel that Berserk has entered a bit of a Dork Age in comparison to the Golden Age arc since Guts' new companions have joined (especially Schierke), introducing things like elemental powers and more slapstick between Evarella and Puck, which have somewhat softened what is still an incredibly grim and violent story.
In addition, many fans aren't very fond of the first three volumes, which mainly consist of Guts being not very sympathetic as he ruthlessly and amorally hunts down apostles in an attempt at reaching the Godhand (Of course some will say otherwise, seeing Guts softening up being not as interesting). It's overall just not considered as strong as the rest of the series in terms of both character handling and art.
Saint Seiya hit the dorkiest of all ages with Saint Seiya Omega. It's not Kurumada canon, it changed the super-suit from metal armor to spandex, it added a superhero school, the eponymous character is rarely in the spotlight(!), and so on. It seems that the writers eventually understood why it was so hated, and gave it a second season that thoroughly reverted all changes.
On the other hand, this has caused a broken base, with people that liked the first season of Omega (including some fans who didn't like the original SS) being unhappy that they reverted things, and declaring season 2 a Dork Age.
Suite is also disliked for its characterization, as many feel that Hibiki and Kanade come across as flat copies of Nagisa and Honoka with a rather forced Vitriolic Best Buds angle that gets dropped so quickly you wonder why they added it in the first place.
Some fans also consider Smile Pretty Cure! this (though it is slightly better regarded) due to its episodic, goofy nature (to the point that it feels more like a spoof of the genre), childish writing (with both the Myth Arc and character growth being non-existent), and what many see as blatant pandering to the Moe crowd. Though subverted as it was alledgedly very financially successful (though mostly only with otaku).
It really says something when the most popular character is a villain (Wolfrun), and not even the main one. It also says something when its first SH Figuarts figure is the Ensemble Darkhorse otaku character (Yayoi/Cure Peace) and not the leader.
Light Novels are stated to be in a Dork Age, with the popularity of OreImo. The growing amount of generic Visual Novel-inspired stories with the same trappings as the genre, as well as overly-long titles, has made people view the Light Novel genre as little more than a place where hentai artists can go to as an easy way to go pro.
The less said about the imouto genre, the better.
Many manga readers feel that the shoujo demographic is in this, as many, many new series are generic slice-of-life Kimi ni Todoke knockoffs. There's also the common accusation that most of them focus more on cliché romance scenes and less on trying to tell an actual story. It's no surprise that very few of them have gotten anime adaptions in recent years, with most of them being flops.
The shoujo magazine Nakayoshi is considered to be going through one, as most of their series in the last 5 or so years are either otaku-bait or a cheap attempt to be Hotter and Sexier.
As The New Tens move on, Shonen itself seems to be in a Dork Age. Of TheBigThree that dominated the Noughties, only One Piece has come out relatively unscathed. Naruto and Bleach, while still technically popular, have both suffered massive backlashes due to many controversial plot developments, with even hardcore fans often having laundry lists of things about the series that they hate. Even beyond their own individual problems, they're sometimes seen as being emblematic of common Shonen problems (Such as a poorlybalanced cast of characters, shocking plot twists that fans feel don't make sense, fights being won through Ass Pulls or brute strength instead of clever strategy, certain arcs and even the whole series going on for much longer than needed and certaincharacters being so powerful that they completely wreck the plot).
Fairy Tail has a large fanbase, and its focus on wizards give it an identity comparable to other popular series.note Dragonball Z being aliens, Naruto being ninja, One Piece being pirates and Bleach being samurai, more or less. However, many longtime anime fans consider it average at best, and its anime was put on hiatus due to sluggish ratings and DVD sales. So far, it shows no sign of becoming as popular as its predecessors. Toriko was for a time considered to be the replacement for Bleach, and was given a massive marketing push. However, its sales only do barely better than Bleach, and its anime was cancelled after only three seasons. In fact, when Bleach and Toriko were cancelled, they weren't replaced by new series, but by instalments of some of Shonen's more enduring cash cows, with Bleach being replaced by Rock Lee's Springtime of Youth, and Toriko being replaced by the unaired-in-Japan Buu Saga of Dragon Ball Kai.
One of the most common complaints across all Shonen series (even One Piece to some extent) is that they're all cliché storms, with most series falling back on the same character archetypes and plot progression while doing little to innovate or improve on the flaws of their inspirations. With Naruto and Bleach in their final arcs, it remains to be seen whether any new series will be able to properly replace them and reclaim the popularity they once held, or whether Shonen will continue to be perceived as a stagnated genre populated by series long past their prime.