Most of our games are friendly to investigation and mystery campaigns. This should be no surprise as our initial release, Terror Network, was built with counter-terrorism investigations in mind. But Crime Network and Horror Show are also well-suited to these kinds of adventures (as is our upcoming project Servants of Gaius). The reason for this is pretty simple: this is one of my favorite gaming styles.
Even when I play or run fantasy adventure games like D&D my focus is mostly on city adventures (with a heavy dose of mystery and role play). It isn't that I don't like exploration or dungeons crawls, but I would much rather solve mysteries or investigate a foe's weaknesses than simply move from one combat to the next.
In my opinion, good mystery adventures are relatively open and aren't on a track. But more importantly, they are dynamic. At least that is the style I enjoy as a player and GM. I like when solving the mystery isn't the only thing going on, when all the NPCs (or monsters) are moving organically and doing interesting things. They aren't just sitting there waiting for the PCs to discover their guilt.
This not only makes some logical sense, it makes for a more lively game. All too often you see people running mystery adventures as if is a static quest against the environment. But at the core of every good mystery are the characters. Everyone from the victims to the guilty (don't forget witnesses) have something important to add to the game. And while physical clues are an important feature of any mystery the true investigation occurs through character interaction. If your characters are fleshed out and your backstory concrete, you have most of what you need to run a game.
Clues aren't just things you find in drawers or amid shell-casings on the carpet, they are also found in the minds of your NPCs. When preparing possible leads (a term I like much better than clues) consider what the NPCs know, what they don't know, who they know, how they know these things, and why they are/aren't willing to talk about them. Equally important make sure you know their motives.
A clue in a drawer is great, but a witness or suspect moves around, has things to do and places to be. Some of them also have an interest in preventing the PCs from completing their investigation (some even have an interest in helping them). This really helps keep the game fun and exciting even if the players aren't having an easy time putting together the pieces.
The trick is to design the adventure with failure in mind. By this I don't mean set your players up for failure. But plan for the worst case scenario. What happens in the players miss a critical clue? What happens if they miss all the clues? In my case I find rather than lead them through the investigation when they falter, it is better to make the consequences for not solving the mystery fun and exciting. Raise the stakes a bit and make your villains proactive. This method won't work for everyone, but it has worked wonderfully in my own experience.
This is where your NPCs can truly shine. Perhaps the killer in your murder mystery is just getting started. He starts killing more and more victims the longer the PCs take to figure things out, finally looking to the PCs themselves for blood if they take an especially long time. In a more supernatural style campaign the murders might be part of a cult's efforts to open a doorway to another dimensions, and doing so unleashes an army of demons on the city. It can be good to have an interesting end-game in mind.
To simplify the process it can help to devise a timeline (something I have used in all of our published material). This charts all the major events that may occur over the course of the investigation and should be subject to alteration if the PCs do things to disrupt it. A timeline can be used to add urgency and drama to the game (a countdown to something awful if the characters don't solve the mystery by a certain time or day).
Whether it is for published adventures or for my own personal campaigns, when I design an investigation I try to approach it as if I were designing a setting. Mysteries take place in their own world where the characters and places create a unique environment for adventure. Think about how all the characters are tied to the mystery and how they connect (or don't connect) to each other. Ultimately it is the interactions that matter so try to make these interesting and even dangerous. Some suspect turn violent when questioned or try to lure the PCs into a trap.
As you run the mystery be flexible and open-minded. I remind myself that there is always more than one way to solve a mystery. There isn't a single path from beginning to end and you should reward players who put together clues and leads in unexpected ways. This doesn't mean you alter the facts to keep things moving. It means if there is a clue and the PCs thought of a clever but realistic way to obtain it, let them, don't force them to go through the hoops only you thought of. Perhaps you hadn't accounted for PCs who check a suspect's phone records. If checking the phone records would yield an important clue (even if it is a clue you haven't thought of but one that would exist) go with it.
As with anything in roleplaying (but especially with Investigations) your mileage may vary. There are numerous approaches to running these types of adventures, most of which are available online. One people often invoke is the Three Clue Rule for example. Take what works and discard what doesn't. Hopefully you will find my advice useful. But if it grains against your style, there is nothing wrong with taking another approach.