Dual Sink with Garbage Disposal Setup
Your set up is missing a critical piece. The disposer elbow (discharge tube). Here is a very good article with plumbing schematics and instructions to correct your issues.



Note: I can't tell from your picture, but is there a sanitary street-t where your waste enters that sewer line? A sanitary tee should be used when connecting a horizontal pipe, such as a waste arm to a vertical riser. This will help move that waste along a little better.