The only thing to worry about are the metal contacts. The brown stuff on the plastic looks ugly but is simply cosmetic dirt. It will not harm the plastic housing.
Brown gunk on the metal is not good. Make sure they are clean and free of any contamination. They may continue to corrode if left as is. From the picture I would worry most about your negative post & the bottom spring contact.Your battery cap clips also should be cleaned to remove all of the brown stuff.
A quick short soak in vinegar followed by a very good fresh water rinse, then a scrub and rinse and then dry using warm air from a hair dryer. You will most likely need to do some scrubbing around your negative post to remove the residue that has collected inside the collar. It may eat the post which is a very bad thing as the post goes through the housing wall. A small piece of soft wood with a blunt end works fine for scrubbing - trim up a Popsicle stick (toothpicks are too short) or use a small wooden bbq food skewer. Or you can use a custom tooth brush - melt the handle just past the head and bend it 90 degrees. Regardless of the tool you create, scrubbing will be tedious.
Once dry lightly polish the contacts with a pencil eraser.
If I remember correctly, the 2 screws on the battery cap can be safely removed to free the metal clips for cleaning. The spring clip in the bottom of the battery well can also be removed, cleaned and replaced via the 2 screws holding it. Those screws do not penetrate the housing wall.
You also should straighten the bent clip on the battery cap.
After it dries I'd also hit it with some PURE liquid silicone (spray, wipe and let dry), or a.....very....thin coat of silicone grease.
Why do you suggest this? What is the benefit of adding grease / oil? I would worry about transfer to the o-ring and batteries.