One of my first experiences running CoC was "The Haunting," a classic adventure included in the core book for many editions.  My players were have some exceptionally poor luck rolling, having failed pretty much every single investigatory roll they made whether it was Library Use at City Hall or Persuasion to interview neighbors.   This didn't stop them from completing the scenario, but it was decidedly less fun as they had no idea what was happening.  At the time, there wasn't really any good advice for what to do in the core book to mitigate such things from happening (not that I can remember at least). 
- Remind players they can Push failed rolls.  When you fail a skill roll in CoC, you can Push the roll, meaning you roll again, but if you fail, then some calamity befalls you.  You fall flat on your butt if you fail a pushed climb roll, you run smack dab into the nightwatchman with a failed pushed stealth roll, or maybe you jump a curb and pop a tire when you fail that pushed driving roll.  Pushing a roll really does increase the odds of success. 
- Don't forget about Idea rolls.  When players get stuck, have their characters make Idea rolls, and give anyone who succeed a hint about how they might proceed.
- Be flexible about where clues can be found.  If the scenario says a clue can be found in city hall but the player goes to the library, let the clue be found at the library is the player is successful.  Maybe the same clue can be found by talking to someone in the neighborhood whose an antiquarian with an extensive collection of maps of the local area produced over the years.  (Maybe we can talk about the Quantum Map instead of the Quantum Ogre for a change.) 
- If a player searches in a specific place for a clue, don't make them roll, just have them find it.  i.e.  If Doctor Watson specifically flips through every book on the shelf, he finds the letter left in the pages of the Bible by Professor Plum.  No roll needed. 
- Make sure core clues necessary for the plot to advance are found.  If a clue from the Library is necessary, the PCs automatically find it, but a successful roll will net some extra information. 
For mysteries and horror, it's critical the players get into the spirit of the game.  Accept bad things are going to happen to NPCs and your character.  Dealing with the horrors isn't a fail state, it's part of the fun.  Make sure the players understand what's happening.  A little mystery is fine, you don't necessarily need to understand the motivation of that Colour Out of Space, but a player needs to understand enough to make the experience satisfactory.  There are too many scenarios with a lot of cool information the Keeper knows about but there aren't necessarily any practical avenues for the players to learn about.