Being half screwball comedy, Hayate × Blade runs on these. Note that this is an extremely incomplete list.
In Chapter 20, after Jun tells Ayana that she and Yuho are half-sisters and they have a touching exchange about being glad that they met each other, Jun dissolves into Inelegant Blubbering. At the end of the chapter, we see Hitsugi and Shizuku (who is tearing up herself) watching the whole thing on a screen. Then Hitsugi gives us this little gem:
"My, my— installing security cameras within the infirmary bedrooms... well done, Tatewaki. However, I feel it could be illegal. Let us turn her in to the police."
At the end of Chapter 34, there's a diagram of the Cat Pastries Hayate's class is making for the culture festival. There are two sub-points:
The end of Chapter 43, where we see Jun whispering disgusting, perverted images to a sleeping Ayana to give her weird dreams.
In Chapter 44, Hayate has an imagine spot about what Yuho would turn into after getting a transfusion of Jun's bone marrow. It also serves as a nice Call Back to a similar moment in Chapter 21, when Jun told Hayate that her "internal juices" were going to be injected into Yuho.
At the beginning of the hiking event, Ayana sees Hayate with Makoto and believes that the former wants to break off their partnership. Needless to say, she's pissed. So pissed, in fact, that she spends the entire event going straight for Hayate and Makoto, taking out anybody who got in her way without even slowing down. She was so pissed, she could probably have soloed Ensuu if they crossed paths. Nothing, not even pit traps, can stop her. Then she getshit by Makoto's Indy Ball and rolls all the way to the bottom of the mountain. Yuri Project says it best:
Things go downhill fast. Specifically, the Indy Ball.