Dishwasher doesn't fully drain
You've got way too much drain hose down there. The drains come in high as they should but all the wrap-a-rounds hamper the draining and the waste just siphons back into the washer. Once the drains start heading down after their high entry, they should connect to the main drain. Rotate those taps for a more direct connection. 
You would be able to get a disposal in there but you'll have to start from scratch with all the drain plumbing. Plan it out.