Okay ... very dumb question here. I am in the process of buying a new DVD player and potentially a new CD player. What are the disadvantages of simply playing my CDs in a DVD player or are there none?

It depends. If your receiver has good D/A converters, and you will be connecting the DVD player to your receiver with a digital connection (optical or coax), then there is no real advantage to buying a separate CD player.

Of course, I love the ability to play 6 CDs on random which is why I have a separate CD changer, but they make CD/DVD changers, too.

Me, I want a megachanger universal player...

And I'd also recommend connecting over digital, unless you've got a very high quality player/DAC.

Be careful when shopping for a 5 disc DVD changer. Many of them (lower end models) are unable to play the tracks of the 5 CD's in Random order. they can play one CD randomly but will not shuffle all 5. I believe the reason might be because you cannot shuffle between 5 DVD's, so some don't let you do that with the CD's.

I encountered this with a Samsung 5 disc changer. The directions said it could shuffle but the player would not do it.