I've been trying to improve at this for a while. The main skill seems to be noticing when something should be made more specific, whether I'm saying/writing/thinking it or someone else is. As long as I notice that I'm being inappropriately vague or abstract it's relatively straightforward to correct that. (Unless I'm actually bullshitting.)

I think the most helpful things have been writing a little bit about all the media I consume,[1] and trying to notice non-specificity in everyday conversation. Other situations that I have found useful [1] for practicing the skill, but are either more tangential or harder to make into exercises, include tutoring/teaching, writing, editing (especially people's undergrad English Lit. papers), reading physics papers.

It's hardly an exercise, but I would just suggest having conversations about media/entertainment,[2] maybe with an interview-ish format. The interviewee and interviewer are working on different sides of the skill. It doesn't have to be a literal competition, but it might help if the interviewer thinks of his role as trying to find a claim that the interviewee can't support with a specific example. A possible script:

What's a movie you saw recently? (Paprika.) What did you think of it? (I really enjoyed it!) Um, okay. Why? (Well… I feel like a lot of movies are weird but also just bad, or signal weirdness while actually being really ordinary or shallow. This one was both genuinely weird and compelling.) What do you mean by that? (Like, it's a movie about dreams that's actually dream-like. Certain things seem really scary or important or have some kind of emotional weight that wouldn't make sense if you thought about it for a second. You end up in absurd scenarios without knowing how you got there or even noticing that it's absurd.) Is there a particular scene you're thinking of? (Well, I think it's part of the movie on a very basic level. (...) OK, there's one scene where a dreaming character walks through a door in their house and end up in some other location, and doesn't even seem to notice anything unusual. I was absorbed enough in what was going on to just barely register the oddness of it. I have dreams like that all the time, at least.) So how does it compare to, say, Inception? (It's almost nothing like Inception, apart from the premise. Inception is closer to other blockbuster action or heist movies than to Paprika.) How so? (The closest thing to something like the scene in Paprika that I can think of is during a chase scene, there's a short segment on an Escher-like staircase. But it seems just thrown in to make the chase scene more thrilling. Both the characters and the viewer notice and understand exactly what happened. They actually draw so much attention to it with some weird camera panning that it's kind of insulting.) OK, so what are some of the other movies you think fail to be properly weird? (Uh…)

[1] My weak evidence for these things working is that, compared to four years ago, I have longer and subjectively-more-interesting conversations about movies and music, which was my goal. (I still don't have people to talk to about the stuff I read, but that's a different problem.) I ask questions during conversations, interviews, seminars, etc., considerably more than I did before. I'm also way better at explaining my research, according to people I've explained it to, but lots of factors go into that.

[2] There's a basically endless supply of topics, most people will have opinions, many people will not have clarified these opinions to themselves extensively, and there's very little at stake in expressing an opinion. This might work with discussing other topics (why do you use software product X?), although I'd still avoid politics and personal lives, where we might trigger more rationalization/defensiveness than introspection. The exercise should still help with the start-up pitch scenario, since the real key seems to be showing-not-telling. You could also set it up as trying to convince someone to consume media object Y.