Ryoji and Hideyasu collectively are referred to as the "Nutty Buddies". This receives a "Funny Aneurysm" Moment when Hideyasu tells Ryoji that he was just using him.
There was originally a rumor going around that the mysterious girl was named "Eve" in reference to the Biblical Forbidden Fruit. After that was debunked, the fandom has settled for calling her "Helheim Mai".
Mitsuzane is occasionally referred to as "Mitch" as an Americanized version of his in-series nickname, Micchy.
Ęsir Fansubs translated the Sengoku Driver as "Wärring Driver" in order to convey the pun behind the namenote It's written with the Kanji for "War" and "Extreme", with their dubbing the Heävy Mėtal Ümlaut as appropriately extreme. When it turned out that the Driver was actually named for its creator, Ryoma Sengoku, and Ęsir changed his surname as well, fans took to calling him "Warren Statesman".
Another nickname relating to translations but not involving the subs this time, Takatora is sometimes called "Hawktiger" because his given name is a homophone for the Japanese words for those animals (though it actually translates as "Noble Tiger"). Of course, Kamen Rider fans would recognize those as two of the three animals which make up Kamen Rider OOO's Tatoba Combo, leading to the creation of a humorous picture of our Overseer with grasshopper legs to complete the trio. Doubles as Awesome McCoolname.
Alternately, some have taken to calling him "OO", since he's one Medal short of being OOO.
The "Energy Riders", for the four Yggdrasill Riders with Genesis Drivers (Zangetsu Shin, Duke, Sigurd, and Marika).
Team PopUp = "Team Sexy", thanks to the Kamen Rider Girls' portrayal.
As of the halfway mark, some have started using "Sour Grapes" as a nickname for Jerk Ass!Micchy since, true to the phrase's origins, he's acting this way out of jealousy over the attention and affection Kouta gets from Mai.
More derisive viewers call him Bitchy-Micchy.
Sid gets the nicknames like Cherry Juice, Crushed Cherries, or Cherry Crush, thanks to Roshuo squeezing him to death inside a cliff face.
The battle in #36 has been dubbed "Melonbowl 2014" because of the Riders invoved Takatora as Zangetsu versus Mitsuzane as Zangetsu Shin.
Kamen Rider Ryugen's weapon is called the Grape Ryuhou note "Dragon Gun", and when he transforms, the Sengoku Driver calls out "Ryuhou, Ha Ha Ha!". Ryuhou is also, although written with different kanji note "Peak" instead of "gun", the name of a character (coincidentally Chinese) from another NichiAsa Kids Time show.
While not a straight example, you have to wonder if naming someone Takatoranote Only the kanji for 'tora' (tiger) is the correct one was deliberate.
Gaku Sano (Kouta/Gaim) and Gaku Matsuda (Zack/Knuckle).
Hideyasu Jonouchi shares part of his name with Jonouchi, whose most memorable trait outside from his hot-headedness was his bond with Yugi. Hideyasu, however, isn't hot-headed. His friend is though... or rather was before he ditched him, making Hideyasu the total opposite of Joey.
No Stunt Double: Minami Tsukui portrays Yoko Minato/Kamen Rider Marika in both human and Rider forms and also performs her own stunts.
Gaku Sano, who plays Kouta/Gaim, wished he could be a character in Kamen Rider Kuuga when he was growing up, now he gets to be The Hero of the series.
Shōnan no Kaze, the band doing the series theme song, are mostly either fans of the series or at least its previous bands.
The actor for Kaito/Baron, Yutaka Kobayashi, was a fan of Kamen Rider Ryuki growing up. Too bad he's not a fan of bananas, but after accepting his role as Kaito/Baron, he tried to overcome his dislike with bananas.
Prop Recycling: The costume for the Hekija Inves from Episode 14 is merely the Byakko Inves's, with a different mask and without the spikes in the back. Becomes a lot more meaningful once you find out the story behind these specific Inves.
Same for Episode 30's Yagi Inves, being modified from the Komori Inves's costume.
Word of God: Its said that they did a lot of Mythology Gags, such as the multiple Riders being a nod to Ryuki, or the omnipresent Yggdrasill Corporation mirroring Faiz's Smart Brain.
Zangetsu is implied to an Expy of Kamen Rider Ouja.
Though that could actually have been a foreshadowing of Zangetsu Shin II.
Mitsuzane (Kamen Rider Ryugen) and Takatora (Kamen Rider Zangetsu) are an Expy of Shadowmoon and Kamen Rider Black.