There may be nothing more uninspiring than the role that is obviously there for exposition alone. The forensics guy, the medical technician, the psychiatrist...the list is a long one. But any role can have exposition put into it, and you have to find a way to make it work. Usually it varies with how good the writing is, but the majority of scripts have some sort of exposition in dialogue to further the plot. How obvious it is correlates directly to how difficult it is to make it seem, it's not exposition, but either way, there is one thing you can count on:

The actor who must get across what is important without it feeling expository.

For tv, medical dramas, procedural dramas, horror movies, thrillers, and just about ANY sci-fi, there's going to be exposition in certain roles. Usually it comes in a couple of different forms--

The Expert and The Historian.

The Expert forwards the plot by spitting out technical information as though it was second nature. The Historian, by making discreet reference to past events. Any role can become either for a scene or part of a scene, and in those instances it's vital to find a way to get the information out without it being obvious.

With The Expert, a few things are critical. First of all, for a lot of stock roles we have to believe this is what you do every day. That doesn't mean you treat the circumstances as though they are everyday, it means you de-emphasize the information that is not important. A coroner going through a routine autopsy may be going through a laundry list of things, most of which don't matter that much. What does matter is that we buy the coroner as an expert and that the crucial information is set apart in some way. What is everyday and what is not? Complex terminology has to feel as though it is completely familiar, and yes, correct pronunciation makes a big difference. "We believe it may be hypoxanthine phosphoribosyltransferse deficiency, but we can't be sure without molecular genetic testing." What?? I know...

But it's also sometimes about making a deeper choice with a stock role. The deeply concerned, attentive psychiatrist is not always as interesting as the bored one who makes a discovery they didn't expect. Of course, it has to be appropriate to the scene, but the contrast between what is commonplace and what is exceptional can be very effective. Take the stock out of the stock role and the exposition isn't as noticeable. 

The Historian, in the same way, is always more interesting when a deeper choice is made. Well written scripts tie exposition in as a by-product of what is at the core of a scene. The better the writing is, the less noticeable the exposition. Horror movies are riddled with difficult exposition, and just because the dialogue is clearly informational doesn't mean there isn't a way to make it seamless. It may seem completely obvious, but sometimes you have to find your own deeper connection to past events, even though they're not written into the scene. Think of it in the context of how most people would only play what is on the page and it starts to make sense how a strong choice can make the information seem more tied in.

I know, it seems pretty basic. It should. It's not a big picture discussion at all, but until you get on set you're your own director, which is to say you have to know how to approach text. Everyone has to deal with exposition at some point, and admittedly it's sort of a discussion about making pigs fly, but it's a skill. The fact is, every piece of exposition has to be disguised in some way or it would seem gratuitous. You're a big part of that.