Ahh, okay. You're right that missing that distinction caused a lot of my confusion. I don't think there's a bug with dialogue, I think it's just my playstyle mashing up against the UI.
I went back and played a bit again and I think what happened with normal dialogues was that I would see "1/2" or "1/3" and think, "okay, so there's two/three dialogue sections in this response" and not "I can click on this item two/three times and get different responses each time." So I'd read the first section, click (coincidentally on the item), read the second section, click, and so on, thinking that I was advancing through one response and not initiating separate responses each time that I clicked. If I still had my mouse over the item when it got to the final response, I would try to click to dismiss it and wind up back on the first response; if I didn't have my mouse over an item at any point during this process, I wound up wondering why the dialogue wouldn't advance or go away.
Adding an option for the normal dialogue to work like persistent dialogue instead seems like a really good idea to me. I read a bit fast and I do just kind of instinctively want to get rid of text as soon as I'm done with it. The option to intentionally dismiss or advance text might also be nice for people who read more slowly, so dialogue doesn't disappear as they're reading; here it would save them having to make their way back through all the other responses if the last response happened to time out as they were reading.
Regarding persistent dialogue, I think what happened to me (and I was able to recreate this in the intro dialogue in the car) is that I would click while the text was filling in and accidentally advance it. I think a lot of games where clicking as the text fills in letter-by-letter will cause the entire dialogue to appear in that window and will only advance if all the text is already on the screen; I'm just primed at this point to expect that to happen, even if the button says "continue." I've played a couple of text-heavy games that have an option for that as something you can toggle on or off in the settings menu, so that might be worth considering if you want to make sure players don't miss that information.
So no bugs! Just me misunderstanding and a couple of usability notes for you to consider.