The high amount of Shout Outs is unsurprising due to Katawa Shoujo's origin from 4chan.
The class overview CG is a good start. Contains at least Lezard, Ikuno, and gender-bent Haruhi. The original release of Act 1 has also Lelouch but he was taken out in the full release, replaced with a more generic-looking guy. The official blog has confirmed another: Ritsu. She was intended to be an original character, but by sheer coincidence resembled Ritsu when K-ON finally aired. Rather than change the design, the developers performed a "retcameo".
Also, the chubby guy in the top right corner looks a bit like Peter Griffin
Tea house Shanghai was originally supposed to be a Higurashi reference, but the devs quickly backtracked and made it a Touhou one instead.
After a conversation with Kenji, Hisao mentions a book he is reading a book about "an underground postal system that may or may not exist", a reference to The Crying Of Lot 49.
It is also possible Kenji was referring to Jet Li's "The One", which has a similar premise.
Hanako is reading a book about "a boy and a tiger on a boat". This is Life of Pi. If Hisao does not scare Hanako away in the library, she'll even namedrop it. At one point, Hanako also reads "Dance Dance Dance" by Haruki Murakami.
When talking to Hanako about a certain book series, Hisao recommends she read the original book, but warns her that the sequels are not nearly as good. However, he does concede that "The God Emperor" is pretty good.
Hisao picks up a random book in braille while in her room. While he is unable to actually read it, the title (not in braille) reveals it to be "Death on the Nile". Lilly apparently likes Agatha Christie's detective fiction.
Kenji mentions at some point that he sees Shizune at Hisao's door, intending to give him his mail, and how he warded her off with the shine from his glasses.
Early on, Hisao says that when they heard about his arrhythmia, his parents "practically had two hemorrhages apiece," a reference to The Catcher in the Rye, in which Holden says something similar about his parents in the first chapter.
Hisao also says "phony" a couple of times during Rin's path.
Ironically, she is one of the girls with no missing limbs.
It's also a trope, with some importance to her development arc, as the good ending requires Hisao to open up with his problems and allow her to grow a little and help him as well, rather than white knighting and therefore expecting to get "something for nothing" out of the relationship.
Mutou bears more than a passing resemblance to the Tenth Doctor and thinks in the same general way that all incarnations do.
Misha quotes President Kennedy at one point during Shizune's path. "Ask not what your school can do for you...but what you can do for your school!" This moment hints towards her fondness of American culture, especially when she also mentions paper football.