If done right, I would enjoy playing such a game. I know there was a crime scene game called L.A. Noire that looked interesting, even though I have never played it. One thing that I am very impressed with in that game are the facial expressions. They look really good and actually are part of the gameplay when interrogating somebody. Based on the Wikipedia page there may be some elements from you idea implemented in their game you can look at, that is if you don't mind the Mature nature of the game.

Just keep in mind that a game as you describe can very quickly generate an unmanageable amount of paths the player can take. For example, what would happen if you accuse a certain person using a gun, with jealousy being the motive. What would they say? How would that change if you used a different weapon or motive? If I were to go about doing this I would probably have the dialog be generated using different parameters. To keep it from feeling robotic, I would try to have custom dialog for commonly chosen combinations, including the solution to the case. Basically what I am getting at is there is a definite technical challenge to be overcome to do what you are describing well. If you could pull that off I would definitely be interested in the game.

Yeah, my first idea was to make a Facebook game, so:

1) you should solve it as fast as possible making less mistakes as possible in order to brag to your friend

2) everyone has to be able to solve a case in a reasonable time.

So, my idea is that, when a case is designed it should contains all the evidences of the murder, the weapon and the motive.

so, when a player makes the wrong choice the system tells him an evidence which should fix a part of the solution.

I'll give an example... let's think the user is playing in the scene from "A study in scarlet" of Sherlock Holmes,

if he makes the wrong combinations about murder,motive and weapon the system says:

"There is no blood of the body in the scene, so the weapon is poison"

if the user makes a second wrond combination the system'll says:

"There is a wedding-female ring in the floor, the mandatory is the gealosy (there aren't sufficent proofs about the woman's name)"

if the user makes a third mistakes:

"the telegram from Cleveland says that the dead man had requested protection from a rival in love that has followed him from America to Europe, his name is called Jeferson Hope, and he is the murder."

So you have 3 chance to solve the case since the 4th time the system has told you all the necessary information to solve the case (showing all the evidence).

I think the score have to be related to the solving time but mainly to the mistakes made.