Summarize:

The official logo is a deep, dark green with noticeable teeth and claws. The top jaw is smaller than the bottom jaw and is angled upwards. The crocodile's tail should be rounded and point in the same direction as the jaw, not at the crocodile. The eye should also look more slit-like than rounded. If the crocodile looks cartoonish and lacks detail, the shirt is a sure fake. Lacoste's Vintage brand is an exception. The crocodile will be high-quality but the same color as the shirt. The logo is a patch that is lightly sewn on from behind. You won't see the stitching when you look at it from the front. Look out for stitching around the patch's border, loose threads, or needle hole marks. These are signs that the polo is a fake. On a few brands, such as the Vintage brand, the crocodile may be printed directly on the shirt. The crocodile will be in the middle of the left side of the shirt. It should be between the bottom stitching on the collar and the second button. Low-quality fakes often align the crocodile with the bottom stitching. That stitching may also appear crooked. A few real Lacoste versions also align the crocodile with the bottom stitching, so don't depend on this one observation. The outline of the crocodile's body should barely be visible. There won't be any colors, threads, or obvious stitching. If the finish doesn't look clean, the shirt is a fake.
Look for detailed features like claws and teeth. Make sure the logo is on a white background. Make sure the logo is under the second button. Turn the shirt inside-out to see the faint outline of the patch.