You have stumbled on the issue (or a primary issue) that prompted the development of the gumshoe system. GUMSHOE is used for a number of games with investigative elements, including Trail of Cthulhu, a GUMSHOE implementation of CoC and Night's Black Agents, a spies-vs-vampires setting with a more militaristic bent. By extension, the solution adopted may work for you, regardless of the system. In a nutshell:

Never make the progress of the game wait for a successful roll

The GUMSHOE answer to this is exactly what's above. Let's get some details on it.

Since it's an investigative issue, it's important that a clue is well defined: A piece of information necessary for players to get to the next scene. That's the GUMSHOE definition and we'll stick with it.

In GUMSHOE, a character with an appropriate skill, in the presence of a clue, who takes an appropriate action gets the clue. There is no roll.

You have a player with a high skill regarding guns (I don't know Delta Green - is it "shooting"? "ballistics"? "slugthrowers"?). The clue is that the bullet holes in the aftermath of the battle are wrong - if they were enemy forces they should be a different calibre - the ambush was by friendly forces! So when your gun-knowing PC says, "I take a look at the bodies to see if anyone is still alive" or, "I try to figure out where the ambushers were located by checking out the trajectories in the rubble" or whatever, you give her the clue.

That's it. Now, there might be more information, juicy details like the fact that the rounds are teflon-coated, a sure sign of Major Tambert's involvement, or whatever. Go ahead and let extra goodies like that be rolled for. They give the players rewards for being good at what they do.

But never stop the game from moving forward for lack of a successful roll. You're just frustrating everyone while they wait for that "live wire".

This isn't about just giving the clue away. There are two conditions that must be satisfied before the clue is given:

• A competent skill-user must be in the scene with the clue
• They must take an appropriate action in the fiction that would reasonably reveal the clue

This provides some measure of flexibility. As GM, you know the nature of the information and therefore what actions would reveal it. You don't just give away the clue for walking into the space. You wait until something has happened that would reveal the clue.

The point is that finding the clue is boring. It's what they do once they know that's exciting. A clue can still be hidden. Papers could be locked in a safe, that safe could require safecracking or demolition to get inside. But if the forensic accountant gets her hands on the papers, and says, "I look for unusual activity in these accounts!" give her the clue - do not roll to see if the forensic accountant succeeds at this time.

BTW - In the above example, if a failed demolition roll destroys the papers, there had better be another way to get the information (or some information that leads to another scene) or you're just as stuck as if you hadn't provided a clue in the first place. A better result for a failed demolition roll has some other negative impact - it takes all of their detcord, for example, but still gets the clue free.

Since you say you're a first-time DM, I might exceed the scope of your question slightly in my answer. You're up against a philosophical question: Are the players co-tellers of the story, or "passengers" in it? This affects whether or not a particular quality is a Pro or a Con.

Players as Co-Tellers

In this approach, you treat the players as storytellers, and your job as DM is to arbitrate disputes between them (like an editor working with multiple writers) and to provide a general framework for this to occur. You keep the 'grand vision' of the world, while they cooperatively tell stories within it.

• Pros of revealing backstory in this approach: The players are able to incorporate one-another's stories into their narrative plans, and can decide how to use their own characters' motivations to further the 'mole' narrative.
• Cons of revealing backstory in this approach: Minor, but if the other players don't like the narrative, they'll be well-equipped to bypass it.

Players as "passengers"

In this approach, you treat the players as mostly reactionary inhabitants of the narrative, rather than near-equal participants in crafting it. This more closely resembles the 'traditional' DM/player relationship, with the players and characters both being surprised by in-game events. It allows more authentic reactions on the part of the players, but can sometimes create tensions since the DM decides how the characters' arcs will unfold rather than the players getting to develop their own visions.

• Pros of revealing backstory in this approach: There really aren't any. It basically forces the players into the co-teller role, which might make your job as DM easier but ignores the whole point of this approach.
• Cons of revealing backstory in this approach: It ruins the surprise and authenticity of the players' reactions, and essentially forces them out of their characters' heads.