Let characters talk before engaging (spoilers for season 2)
A thing that bugs me, and I've been guilty of this too in the past, is when people just rush in before letting a character finish talking. When it's during a choice, granted, you're paying more attention on what to pick rather than listening to any talking anyway, but this also refers to when you approach a character, and their dialogue being cut when you trigger the scene. Did anyone listen to John doing impersonations of Batman and Gordon on the roof? Absolute golden stuff!
When you find John at the funhouse in episode 4, he talks to himself (and to the Agents) about how this place was special to him and Harley, how the Agents rudely showed up uninvited, and his brief doubts on whether Bruce sent them. Pretty interesting, and could potentially help you decide on whether to trust him or not by the way he's acting.
In the vigilante ending, when Avesta is on the rooftops, you can hear her speaking to her mother, and part of the conversation is in Farsi, which is a language spoken in Iran. Honestly, I had no idea she spoke Farsi, but later found out she worked over there, so it makes sense. In the villain ending, she only says one word of Farsi, which is when the bomb is defused in the church.
My favourite one however is in the vigilante ending when Bruce dresses his wound, Joker will constantly bother Alfred with questions about Bruce, Alfred's accent and John's attempt at doing a British accent, and how'd he haunt Bruce if he died. I recorded the conversation and edited out the silence, so you're not waiting for them to speak. It's in 2 parts because I forgot a piece of the conversation.
http://bandicoot88.tumblr.com/post/172333568276/yes-i-did-listen-to-everything-joker-had-to-say
http://bandicoot88.tumblr.com/post/172596690138/i-was-pointed-out-that-i-actually-missed-a-piece
Post your own favourite moments. 
Comments
Yeah i never rush the dialogues anymore because you can miss some really good moments,my favorite one is when John is on the roof talking about Gordon's mustache.
Don't forget John and Bane bickering in episode 4.
I'm glad you brought this up. Most people skip these kind of dialogues
I like to wait and listen before engaging too though it may lead to situations when there's an awkward silence afterwards, because you were supposed to move while the person's talking.
I also usually wait right before the timer runs out to choose a dialogue option to hear most of the dialogue. You may miss some fun conversations otherwise.
i never rush a telltale game because of this. I also always wait until the last second before choosing my dialogue option.
It really bothers me when youtubers just rush through everything, especially stuff like this.
I skipped all of them in my first playthrough but in my second i thought... why not? Let's just wait and see what they have to say. Loved Joker's british accent lol, totally worth it to wait five minutes for the conversation to end.
I always wait to see when the character stops talking. In a second playthrough I’ll time my response or walk up based on the timing of when they stopped talking.