OK, my 2 cents worth ... I agree with everything INCLUDING changing the needle. BUT, I only saw one answer about how to tie off 'good' stitches when taking out the bad ones.
I was taught to pull out (don't cut/rip) enough thread so you have top and bottom threads long enough to put into a hand sewing needle. Pull top thread to the back, put in hand sewing needle, make a couple of tiny stitch through backing and batting only, then insert needle in between the top and bottom, for about an inch or two, pull thread a little tight, trim thread and ends of thread will be pulled back into the quilt when you release the tension you had on the thread.
If that doesn't make sense, PM me and I'll try and explain it better.