Hi
Would there be any trouble should I decide to use both 3.3V and 5V voltage pins of Diecimila at once to power different components? I'm just not sure it can handle providing power to both of the at the same time.
Yes both are avalible for use at the same time. Big thing is to be aware of the current limits avalible. A data sheet on the 3.3v requlator will tell you it's maximum output current, I think it's only 50ma or so. The 5 volt regulator is a 1 amp ouput model but the Arduino board consumes a little of that.
Would there be any trouble should I decide to use both 3.3V and 5V voltage pins of Diecimila
You can't get 1A from the 5V regulator even though it is rated at this without a heat sink it will get far too hot and shut down at anything approaching about 500mA. You can only get this from the USB port. I would recommend 350mA maximum from a 9V supply (less for a 12V)
Ok, I'll stick to a single source 
Thanks guys 