I have repaired several old quilts that were deteriorating or had mouse holes clean through them. Just lovingly handle each area and don't be in a rush.
The most important thing I would recommend to you is that you use old, soft fabrics to do the repairs... fabrics from old clothing. New fabrics would be ghastly on a quilt like this and would stand out like a sore thumb. If you can't find old fabrics that would work, at least use something like cotton lawn which is thinner and softer than regular quilting cottons.
It's definitely worth saving, but I wouldn't plan to ever wash this quilt again. It should be on display only... bed, wall or hanging draped over something.