Apple logo on laptop case is flashing when in sleep mode!

Hmm... that's a good question. The Apple logo is simply a cutout in the case that lets the display backlight light up the logo... which means your display backlight is going on for some reason while in clamshell mode (which is what I would imagine you mean by closing it without putting it to sleep) as well as when you actually put it to sleep. When you say "close the lid withou putting it to sleep"... do you have an external monitor and keyboard connected... or are you using some sort of third party app or hack to prevent your MacBook from going to sleep when the lid is closed?

Are you using a bluetooth keyboard and/or mouse? You may want to check to see if "Allow Bluetooth Devices to Wake this Computer" is checked in the Bluetooth preference pane:

http://www.wap.org/journal/macbluetooth/BTSettings.jpg

If it is... try unchecking it and see if that helps.

What is happening is that your machine is trying to go to sleep and then waking up - repeatedly. If this continues it will damage the machine. Check your logs to find out why it isn't going to sleep. What kind of keyboard is it? It sounds like the keyboard is waking it up. If you really don't want to run it in "closed clamshell" mode, unplug the keyboard.