Something else, from a structure perspective. I think I first saw this in the Gamma World d20 GMG, but I'm sure it's appeared elsewhere (although maybe not in gaming).
Simply phrased: If the the mystery does not have to have a specific answer the third one the players suggest is the correct one.
This simple phrasing, needs explanation, however.
In a murder whodunit, ala Christie, the actual murderer is generally interchangeable with the rest of the suspects for most of the story. A mystery needs to present multiple plausible suspects. So you structure the plot so that the clues point to, say, six possible people. Let the players assemble the clues as they wish. When they investigate the first person, the evidence doesn't hold up. They get a few more clues that lead them to a second conclusion. When they focus on the second suspect, everything looks good, but he the case falls apart when it's revealed he's covering up his affair with the victim, not his guilt in her murder. This drops some more clues, however. Then when they talk to the third person, it all works and they have their murderer (or mole, or theif, or whatever). This requires a little thought and some notes, but it's not particularly hard. Also, just because the target will appear later as a reoccuring villian or a rival or needs to lead them to the mastermind, doesn't prevent this structure from working. It only really falls apart when you need a specific person (player's mentor, sibling, girlfriend, etc) to be the villian.
The second thing is if it's ALWAYS the third thing they try it gets obvious fast. So change the number frequently, or pick the number randomly by rolling 1d4 or 1d6 or something. Depends on the patience of your group.
This structure works for a lot of things beyond a whodunit. Find the mole, find the location of the missing temple, etc. The key is that it works as long as the specific answer isn't as important to the plot as the search for it is.
Also, having someone kick in the door to try and kill or threaten the PCs works, as does the foil showing up and putting the moves on the detective or whatever. If the players are lost and confused, have the world give them direction. Again, don't limit yourself to having the killer try and take the PCs out because they're getting close. Maybe they kill someone else. Maybe they try and flee to country. Maybe the assassin makes an attempt on their target with the PCs in the room. The details depend on the plot and the mystery, but have a NPC act so the players can react and then follow the new leads and clues.