Criminal Case Ranks

first of all, the best thing you can do to progress faster in this games is to have more "teammates"
Receive rewards/gifts from facebook shares
now that you have tons of criminal case facebook friends (see link above), you can take a look on their facebook wall and click every criminal case share they have on their wall. every one of them will give you something. The daily limit for energies are 3 pieces of orange juice and 1 pieces of potato chips. If you what you see and click on their wall is not enough, you can search for game related groups and pages that usually get clogged with shares and will get you what you need in no time.
Share rewards with other on facebook
You get what you share. When you share an item with another player - you get rewarded just as much. so the same method applies here as the previous note, share at the same place you found other share. now you know why they share :)
Level up faster
Play any scene and 5 stars, so you can play this scene with 5 energy points instead of 20 energy points. You get 20 XP for each scene that you play, this is a great way to level up with the least amount of energy. In this way, you can skip a level very quickly
Solve cases
Solving cases is not for the benefit of man kind. don't jump from one place to other, finish what you started. it gets you places in the game - faster. It takes 36 stars and 4 scene to solve a case.