Totally Awesome Pirate Brain
The dice control the flow of information, and some rolls should (statistically) fail, but to solve the matter requires the players, not the dice. In 5e, the dice are unlikely to fail, and the players always have the skills they need.
Did I explain it better?
Maybe, I'll lay out a scenario and tell me what you thinkl.
Lets take a look at a good solid murder mystery. I'll grab the basic plot from Agatha Christie's Murder on the Orient Express. We'll set it in Eberron and the adventure is now Murder on the Orien Express (I'm brilliant!). The lightning rail starts in Sharn, and doesn't stop until it reaches Flamehold in Aundair, roughly 1000 miles away.
Here's the scenario, largely cribbed from the Wikipedia entry for the novel:
The Scenario said:Early in the morning, party is wakened by a cry from the vicitim's compartment next to theirs. The wagon conductor responds by knocking on the door and a voice from inside responds in Elvish, "It is nothing. I am mistaken".
In the morning the victim is discovered, the an Orien representative on board asks the party to investigate (who care why, its D&D lets just roll with it for now). The party determines that the victim has twelve stab wounds. The window is left open in the victim's compartment, presumably to make the investigators think the murderer escaped out the window, but there are no footprints outside the window in the snow. A handkerchief with the initial "H" is found in the compartment, a pipe cleaner, a round match different from the matches the victim used and a charred piece of paper with the name "Armstrong" on it.
I'll pause here, at what point do we use Skills to find any of these things? A search should make them obvious. The next section is where I'd use a skill though.
The Scenario Con't said:The piece of paper with the word Armstrong on it helps the party figure out who the victim really is and why someone would want to murder him. A few years back, a man named Cassetti kidnapped a three-year old girl, Illidra Armstrong. Cassetti collected a ransom from the wealthy Armstrong family, but killed the child within two hours of kidnaping her. The party concludes that the victim is actually Cassetti. The voice in victim's compartment could not have been the his, since the victim spoke no Elvish.
I'd use some skills to put together than 1) the burnt paper refers to the kidnapping and murder, 2) Cassetti is the victim and 3) Cassetti doesn't speak Elvish so somebody else was there.
We go on from there. I wont spoil the actual killer from the novel but skill uses should reveal facts about clues rather than obvious clues themselves. So, talking to a suspect should get some facts, it would be skill checks that help determine truth from falsehood. Going into a murder scene and searching should produce all available an obvious clues with skills providing less obvious links between clue or what the clue actually means.