A jar of sauce should be good for about a week after being opened if kept refrigerated. Moldy food, or food in a container growing mold on the lid, should be tossed - without smelling or tasting it!
As for storage of leftovers - storing a whole jar in the freezer that is only half full is a half a jar of wasted space. Depending on how much you will be using at one time - I would put it into 1 or maybe divide it up between 2 or 3 zip-top freezer bags. Just put the sauce in the bag and seal it almost all the way shut - carefully squeeze out as much air as you can and finish sealing. You can then lay the bag(s) flat in the freezer until frozen and then store upright if you wish. This is the most space efficient method that I know. This is how I store my homemade tomato sauces, stews, chili, etc. And, a flat slab of something will thaw quicker than a block of something.
"It ain't what you don't know that gets you in trouble. It's what you know for sure that just ain't so." - Mark Twain