GE Dishwasher Dirty Glasses/ Filter Drain help

Hi - I have a 12 year old GE Profile GSD3200. After a cycle, the glasses are disgustingly dirty. I've removed the back grate and cleaned the screen. Now I've removed the center grate (which was full of mold/mildew) and there is a drain that might be covered by a bowl shaped filter but the entire thing is full of dirty moldy mildew gray water. Is it a filter; how do I remove it? Is this a drain problem? Any help is appreciated. - Shelley