Kamen Rider Den-O is a series about time travel. In an alternate timeline where she never met her astronomy-loving boyfriend, the main character's sister gives her cafe a flower theme, instead of an astral one. A character from the future is revealed to be her daughter. Her name? Hana, which means flower.
Towards the end of Ore, Tanjou!, the DenLiner makes a sidetrip to the time when Ryotaro was born, allowing Ryotaro and his younger self to see his parents for the first time. Hana is also seen looking out the window as well... because it's her first time seeing her grandparents.
Den-O's form when possessed by Sieg is the Wing Form, meaning he uses wings to attack. Sieg is a swan-themed Imagin. Swan wings can break human bone.
At the end of the series, when Ryotaro believes the 5 Heroic Imagin he fought alongside have vanished, he calls the names of all of them...except for Sieg. At first I thought this was just because the writers had forgotten about Sieg in that exact moment, but then I realized why: Sieg has spent the shortest amount of time with Ryotaro - the number of episodes he appears in can be counted on one hand, and even if you include Ore, Tanjou!, that's still less than 4 appearances at this point; unlike the 4 Taros, he has not made that many memories with Ryotaro, so it makes sense that Ryotaro wouldn't miss him that much.
Some of the enemy Imagin are based on riders from Ryuki - the Bat Imagin is based on Knight, the Crust Imagin is based on Scissors, and so on. However, the titular rider (and for that matter, Ryuga) from that series doesn't have a corresponding enemy Imagin. This might seem odd...until you remember Ryutaros's dragon motif - if he hadn't decided to change sides because of his feelings for Airi, he would be an enemy Imagin, and if he hadn't named himself, he would be the Dragon Imagin!
Also, Sieg fills the position of Swan Imagin, giving Femme a counterpart in this show. Really, the only Ryuki riders not associated with Imagin are Tiger, Imperer, and Zolda (although if one counts Deneb, Zolda does somewhat have a representative).
It might seem odd that Deneb possessing Kotaro/New Den-O results in New Den-O Vega Form, whereas him getting possessed by one of the Taros' results in Strike Form wielding a weapon based on the Taros possessing Kotaro, but if you think about it, it makes sense in-universe. Unlike Den-O, Zeronos doesn't need to be possessed by an Imagin to access Altair Form, as Yuuto's will is strong enough; as such, Vega Form acts more like a Battlizer as opposed to one of Den-O's forms. Additionally, the weapon that Deneb would presumably transform into for Strike Form, the Denebick Buster, is associated with Zero Form, not Vega Form. Additionally, since Deneb doesn't have a button on Den-O's belt, one can assume that, by extension, if Sieg was to possess New Den-O, New Den-O would transform into Wing Form as opposed to Sieg becoming a boomerang.
It might seem odd that Momo calls his special attack "Part 3" in Episode Yellow, considering that in all other movies and crossovers he's been in, he'll usually give it a special name. Well, there's a reason for that - Episode Yellow is the third part of the Chou Den-O trilogy.
It might seem odd that the crew of the Denliner and Kotaro were able to fool Kuchihiko and his underlings, but aside from Rule of Funny, there's a perfectly logical explanation for this: they've never been outside of their own time period. As far as they knew, the future COULD have looked like the fake one that the Denliner crew and friends were putting on.
The two main forms used by Zeronos are called Altair and Vega, and Vega specifically is accessed by cards tied to Sakurai (Yuto's produce Zero Form instead). The names are also the stars associated with "The Weaver and the Cowherd," one of the most famous sets of Star-Crossed Lovers in folklore, and underlines the impossibility of the original Sakurai ever returning.
Considering that the majority of Kamen Riders are not singularity points and/or lack gear that can protect them from space-time abnomalies, it's rather fortunate that Den-O ended up being the one who dealt with them.