Urabe's "Hates Being Touched" running gag will become a plot point.We already know that it's not because of sexual abuse, since she has already stated outright that the "voice" at the beginning of the story told her that Tsubaki would be her first intimate experience. Plus, she has allowed Tsubaki to touch her once he's asked permission. However, probably that aspect of Urabe's personality stems from some big secret in her past (which might be a little darker than the pasts we've seen for some of the other characters to date), and involves her parents in some way, since we scarcely hear anything about them and have never seen them, and we do know she's gone to visit her father separately from where she's established as living.
The relationship between Urabe's parents was similar to her own with Tsubaki.She grew up seeing her mother domineering over her father and believed as a result that that's how normal relationships work, and it's simply playing out afresh in her own relationship with Tsubaki. (Though she's not above being an Aggressive Submissive.)
Tsubaki will eventually get to meet Urabe's family.And in doing so, he'll learn that her parents are even more quirky than their daughter (for example, her father will either be a comically Overprotective Dad, or else he'll be a Bumbling Dad). Regardless, that family meeting will be another milestone in the duo's relationship, as Tsubaki will want to get Urabe's parents' approval.
Tsubaki and Urabe's First Kiss will be a MAJOR plot milestone.Specifically, it'll happen close to the end of the manga, probably when they are close to graduation or going to enter the same college together. Then there will be a Distant Finale where the two have gotten married and have had Their First Time.
Urabe spewing mass drool when overly happy will happen again.Remember the pilot chapter, where Urabe said that when she's extremely happy, she spews out a lot of drool, and a demonstration was given? It hasn't happened since then, indicating that in-universe Urabe has possibly learned to master some control over that reflex (and in real life, that pilot chapter was originally intended as a one-off story), but there's going to come a chapter where she's so overcome by happy emotion—concerning Tsubaki, naturally—that she just gushes. Probably during their First Kiss or maybe earlier or later, depending on what the mangaka decides.