My first few bindings were pretty awful, but then I practiced on a few sample squares using tips I had gleaned other quilters. Now they are easy for me. (I too "trimmed" a corner once! shudder.... never again.)
One of my problems was controlling the quilt top. Finally I developed an approach that most quilters don't use, but that works really well for me. Instead of cutting the quilt top edges, I use a Sharpie to *mark* the quilt edge. When I machine sew the binding on, I act as if that marking were the quilt edge. What this does for me is control the quilt edge so that edge is not wiggling on me as I sew; the quilt is very stable.
Regarding mitering corners, I *finally* realized that however much a seam allowance I am sewing for the binding is *exactly* how far away from the edge I need to stop. It needs to be EXACT; not one stitch more or one stitch less. Once I mastered that idea, my miters started looking nice.
I do not prewash fabrics, and the same applies to binding fabric. The sizing in unwashed fabric helps stabilize the binding. If you prewash fabrics, you *really* need to starch your binding fabric before cutting it (assuming you are doing straight-grain and not bias binding) into strips. This keeps the binding fabric from stretching and twisting while you sew. I do not use bias binding unless the quilt edge is scalloped or curved.
Hope some of these tips help.