Oh what a beauty!! I would finish it. She sure put alot of work in to it. Its a beautiful family heirloom!!

It looks like a lot of pieces are already sewn to make up more blocks, so if at all possible, I would finish it. I wouldn't want holes, so I'd either re-do those areas, or applique over the holes, as someone else suggested. The quilt is really lovely, and I think you will cherish it once it is finished. As a ufo, how much are you really going to appreciate it? Also, if it remains in pieces, someone in the future may just trash it all, not knowing what it was or what it really meant to them. Once it is a finished item of some sort, you can attach a label to it so descendants will know what it is.

I agree with mic-pa and Dina. Fix what you can (or want to) and finish it the size it is. Are there enough pieces in the box to make something for the others she meant to make a quilt for?

what if you patched the little holes with white fabric on the back. I love it.. I would hand patch the white holes and then leave a story about it on the back fabric...then who ever ends up with it after you will know why some holes are in it..

How about appliqued hearts over the little holes? The hearts would show that she made it with love...even if it isn't quite perfect.

This may not apply to the situation above, but a quilter had left behind some unused pieced blocks. One of the quilter's daughters or a female relative used them as appliques in different quilts which were then given to relatives. I saw an exhibit of them in a show a few years ago. It was nice.

Oh golly! That quilt is beautiful. PLEASE finish it. Rip out what is loose and re-sew it. You won't be sorry. There is a ton of work put into it. I have 2 that my Mother-in-law made. Wouldn't part with them at all. Just a little at a time, so you don't get worn out or tired of working on it.

That is a beautiful quilt your Mother began. She probably didn't get it finished as it was a lot of work and time consuming. We all get burned out on some of our projects. Maybe she did on that one.
If it were me, I would repair as needed and have it LA. It will truly be a great heirloom in the future for someone in your family! Go for it. Forget the quilt police!! Nothing is perfect anyway. Best wishes on your decision...

Finish it. Fix the seams where the fabric was missed entirely. Also, it might help to iron the seams open and SITD on both sides of all seams when quilting to help stabilize the seams.