I always pin my intersections so they are correct.
My 1/4" seam isn't so accurate-I tend to use the edge of the presser foot as my guide. If I try to sew a block on 2 different machines I'm in big trouble.
But anyway, I pin my intersections so they are good. When I sew the block together I tend to have to trim it and hey, you know it's supposed to be a 6.5" block, but it's going to be a 6" block and I just trim everything so it matches.
You may want to play with patterns for awhile that don't have seams you have to match. Like a lasagna quilt or this one:
http://quiltville.com/crayonboxpf.html Just to get the enjoyment back and then practice on small projects for awhile. A lot of time it just requires a little patience and allow yourself to take your time.
On the other hand, I envy you the ability to paper piece. I've looked at it online and just cringe thinking it looks so hard.
Do what you enjoy and find a quilting buddy to help you put your blocks together.