Include clues, but don't make them vital to understanding the story. Have them along as vignettes for extra information. If you want them to contain important plot stuff, ensure that the information is also delivered via the contact dialog or something similar so that the player isn't left going "huh???" at a development because they didn't end up reading the clue.
Most people really will ignore the clues, barely even realizing they exist.
Though, there will be a minority of people who always sift through the details. They're likely going to be the ones leaving you most of the feedback.
If you want my take? They're a nice addition, but never a necessity. If you can think of good, or even clever or quirky, ways to use them, I'd definitely say go for it.
Use clues! I love clues! I always read them. They really help immersion in the story. If you have a multi-mission arc with no clues at all, it feels like something's missing. There is such a thing as too many, but I think crucial story elements should have clues. You get 100 characters for objective completed text, which isn't much to work with. A clue can make "You found an old journal" far more interesting. Your bosses and captives can actually give me some real information in clues.
This goes doubly so on teams, as only the person grabbing the blinky gets to read the text, and NPC dialogue gets pushed up pretty fast with rewards and "you have defeated" messages that show up by default in the same window. Not everybody makes a separate tab for NPC dialogue.
Just keep in mind that you can't control the order in which players receive them, unless you're using triggered objectives, so the clue I get from the boss at the back of the mission should still make sense if I missed the one from the blinky at the front. I've run a few arcs where clues referred back to other clues I hadn't gotten yet.
On the subject of clues: What determines the order in which they appear in the player's clue list? Is it the order in which you place your objectives in the MA editor?
Eva Destruction AR/Fire/Munitions Blaster
Darkfire Avenger DM/SD/Body Scrapper
Arc ID#161629 Freaks, Geeks, and Men in Black
Arc ID#431270 Until the End of the World
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On the subject of clues: What determines the order in which they appear in the player's clue list? Is it the order in which you place your objectives in the MA editor?
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If I recall correctly, yes.
I use clues to flesh out my arc, put in hidden gems or some humour. Sometimes I use it to reinforce the arc or make it more obvious what is going to happen next so the smart player is rewarded for reading the clues.
In multi-mission arcs I label the clues with the mission they were found in, so someone who wants to catch up on the story in a later mission can at least know what they picked up and when.
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My arcs: Dream Paper (ID: 1874) | Bricked Electronics (ID: 2180) | The Bravuran Jobs (ID: 5073) | Backwards Day (ID: 329000) | Operation Fair Trade (ID: 391172)
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I have recently been struggling whether or not to make use of clues in my arcs. I feel like they can be a nice way to advance the story of an arc, however I worry that players often never realize they get them (esp. on teams), or forget to check them, and that these end up getting lost in the shuffle.
Is there any specific advice people have about how/when to use clues to the best effect?
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I'd take the time out to put clues in. While a lot of people won't check, if someone does, they'll see the clues there. It'll give your arc a more polished professional feel. If you have a glowie, fill in the clue text with a sentence or two. If something is mandatory to complete the individual mission, fill in the clue text. It only takes a few moments, but can impress the people who do check for those clues.
Arc ID#30821, A Clean Break
The only problem with defeating the Tsoo is that an hour later, you want to defeat them again!
"Life is just better boosted!" -- LadyMage
"I'm a big believer in Personal Force Field on a blaster. ... It's your happy place." -- Fulmens
I use clues a LOT. A LOT LOT.
I generally try to sum up the general idea in the mission complete return dialogue, but for the real, nitty gritty details, the clues HAVE to be read. On my Arc "The Wretch's Gift", I tell people up front they need to read them to get a good understanding of the story, as Wretch isn't known for his public speaking 
I'm only ladylike when compared to my sister.
Use Clues. then have the exit pop up say something like "What's that stuck to your foot? Could it be a CLUE?"
Yes I've actually done that. 
My first short story (detective fiction) came out in Jan-2012. Other stories and books to follow, I hope. Because of "real writing". COH was a big part of that happening.
I have recently been struggling whether or not to make use of clues in my arcs. I feel like they can be a nice way to advance the story of an arc, however I worry that players often never realize they get them (esp. on teams), or forget to check them, and that these end up getting lost in the shuffle.
Is there any specific advice people have about how/when to use clues to the best effect?
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One of Six, Cannibal 6