So I have a crack in the disc in my binding and it caused it to turn and change the angles of my bindings when I'm riding. I figured it happened because my screws were too loose and it caused them to wiggle and crack the plastic disc. I have heard they are under warranty from Burton if I bought the bindings from them. Should I get a new disc or just keep my screws tightened and not worry about it?
Get a new disc. Your binding are a very important part of your equipment and can have a huge effect on your riding. If Burton does not cover it, just go down to the nearest snowboard shop and they should have some extras laying around that they'll sell to you.
You can either head to a shop like Technine said or if you do not mind waiting you should email Burton for a new disc. They should send you one out for free, I got one from Flux as a spare without any problem.
Burton does cover baseplate damages. Give them a call or better yet, go to a shop that carries Burton products. The shop should be able to give you a spare set. The shop should be able to send the damaged plates to Burton for compensation.