He can use his X-Ray Vision to look at a mermaid in the Maid Cafe. The X-ray vision works realistically, so instead of seeing her nude, he just sees her skeleton. Despite this, Date still seems to find her bone structure arousing. Examining her bones enough times earns you the "Bonephilia" achievement.
There's a Running Gag when looking at the lanterns in the Kumakura office while Iris is present: Date will ask Iris if the lanterns remind her of anything, and Moma will bluntly give away the answer ("What, like a dick?"), much to Date's annoyance.
Related is how often porn is used to help win the firefight sequences; in the majority of them, Aiba tells Date there's porn to give him super speed for a moment. No, seriously., but the kicker comes when one sequence involve Aiba telling Date to toss a porn magazine to bait some stupid goons. It works, but what makes it funny? Date cries for the magazine.
Most of Aiba's Somnium entrances are quite ridiculous:
Later on, Moma asks to see her panties; this time, Date just tells Iris the truth, but she doesn't believe him and hits him instead, while Moma denies what he originally asked.
And lastly, during the epilogue, Moma wants to motorboat Iris. Iris tells him to close his eyes... and then switches places with Moma's fat lackey. Moma can't tell the difference.
Meta example: The A-Set twitter has been active since the game's release, and posted this picture. The very next day, the voice actors for Iris, Mizuki and Ota replicated it.
Iris's Somnium is presented as her hosting a Let's Play of her favorite video game, ShovelForge, with her usually bubbly attitude fully intact and lots of Narrating the Obvious. If you run counter to her instructions and deny the existence of Naixatloz, she'll puzzledly remark on the game glitching up on her and even suggest her "audience" take a break to use the bathroom while experiencing Loads and Loads of Loading.
Examining the pond in So Sejima's yard often has Date exclaim that he's just seen some mythical creature, among them a kappa and a merman, only for Aiba to reply that since So is so rich, it's no surprise that he has his own creature. Continuing to examine the pond will have the creature in question (unseen to the player) say something, leaving Date utterly bewildered.
In the flashback where Date decides to train Mizuki in self-defense, he asked Mizuki to throw a punch in order to assess her strength. When she did as he said, that punch was powerful enough to create a shockwave that kicked up the dirt surrounding her. Date went Blank White Eyes and subsequently ordered her not to hit her "master".
A later flashback shows Mizuki effortlessly destroying multiple training dummies before knocking down a tall tree on the grounds of Ikume Shrine. Both Date and Mizuki made a run for it after hearing the priest's angry shout.
After finding Mizuki Bound and Gagged in a hollow speaker in his apartment, Date proceeds to remove the tape from her mouth, leading to Mizuki complaining that he was doing it to forcefully. Date decides to put the tape back on to shut her up while he undoes her restraints.
During Hitomi's Somnium, choosing to shout down a hole will have Aiba screaming "Date likes Hitomi!"
In the epilogue:
Mizuki and Date got into a fight over the former making omelets over-easy. After spending some time using Iris as the intermediary, they finally decide to make up and Mizuki demands various things from Date, including... a new iron pipe.
The first thing Date and Iris see upon entering the Kumakura office is Moma wailing uncontrollably in joy, revealing that he had been praying for many days straight when Iris was undergoing surgery and thanking God for helping Iris recover