Pros:
Puzzles - varied in type and difficulty, these are what you bought the game for. Don't expect anything extremely difficult, though.
Plot - trying to crack the case of a serial murderer who leaves puzzles in his wake, you can get somewhat absorbed trying to figure out the killer's identity. However, it's not a strong enough plot to stand alone
Cons:
Hints - there's very little downside to using hints. Additionally, using hints removes almost all challenge from advancing the plot
User interface - text input uses a virtual typewriter with very tiny keys. There is no left handed option for the touchscreen, making some actions quite inconvenient for lefties
3D effects - the cutscenes and puzzles do not benefit at all from a 3D screen
Length - I've completed ~90% of the game in 3.5 hours. Unacceptable for a $40 game
Other thoughts:
In other puzzle/adventure games, puzzles emerge from the plot. In Hollywood Crimes, most of the puzzles feel like they were thrown in to take up the player's time between story segments.
Conclusion:
With other adventure/puzzle games, the plot is generally good enough on its own to hook the player and long enough to leave the player satisfied after completion. Hollywood Crimes is just too short to give any feelings of accomplishment.