Anybody who's seen my Facebook page lately has probably picked up on the fact that my newest game obsession is Criminal Case. 60 million people have at least tried it. You should totally join the club.
Tip 1 Use the magnifier early in a scene - 1st two stars or so. The magnifier shows you exactly what the object you're looking for should look like including correct orientation. For example, it can show you that an Ace should be upright and red hearts or flat on the ground and black spades. There are only 30-60 things that commonly show up on any given scene. The ones that have the Time Attack bonus round have the higher number of items to find. You can memorize most of the basic items through the first two stars, which depending on how good you are could be 3-5 games on average.
Tip 2 Definitely have some FB friends to Unlock levels. Okay, so I'm a cheapskate. I don't want to have to pay to have the next level unlocked. I'm also impatient, so having ~10 or more FB friends to write reports for you will help.
Tip 3 Save the last star for the second game you play after coming back to it after a significant break (several hours). Typically, somebody will have all 5 hints for you, so you won't have to pay 1500 gold to get that bonus. Each unused tip adds 20K to your score, so these can add up quickly. The first game you play at any time is usually going to be a warmup, especially if you do this early in the morning. Wake up. Drink Coffee. Then play. You can really only earn the "best scores" on the fourth and fifth star because there are more objects to find and you'll have had plenty of practice in the round.
Tip 4 Play on a phone + computer. For some reason, the accounts sync but your energy is unrelated both places. I didn't learn this myself, but it's an awesome trick.
Do the last two stars of Time Attack close together. By that time, you're probably an expert on where most things are on that scene. You may as well take advantage of the muscle memory.
Hope that helps. Have fun. Find me on FB and be my friend. We can be Criminal Case obsessed together.