Get rid of that abomination accordion piece in your drain line, but that would tend to grow smelly in the sink, not below it in the cabinet. It's almost impossible to flush clean. The disposer grinds up food into small particles. Some of them will get lodged in the folds. It is above the trap so there's not much to prevent that smell from rising up.
My original disposer ended up corroding at the mounting bracket to the sink. It wasn't obvious until one day, it literally fell off of the sink. I replaced it with a better quality unit with SS guts. Take a very close look at where the disposer attaches to the sink. What I think caused it was that my DW wasn't getting hot enough water and the powdered detergent didn't always dissolve completely, and particles of it are caustic to the aluminum body of the disposer...causing it to eventually rot away. After seeing that, I switched primarily to a liquid detergent until I added a hot water re-circulation system that provided hotter water more reliably and made sure that the DW heating option was turned on.
Another thing to look at is around the sink. Is the sink a drop-in or undermount? Depending on how installed, there could be a small leak around the rim and keeping the edge underneath damp.
Last I can think of for now...depending on how your faucet is mounted, sometimes, they can develop a leak underneath them. Or, depending on how installed, the gasket or plumber's putty may not be keeping moisture out from underneath.