Picking up stitches around a rectangle for a mitered border

I am preparing to pick up stitches around a rectangle for a mitered border. Two ends of the rectangle have live stitches that are on holders, so that should not be a problem. My concern is about the corners of the rectangle. Is there anything special that I should do when picking up stitches at the corners? I will be working a mitred edging in twisted rib. I would like to avoid the unsightly puckering that I see on the corners of some knitted garments. Also, I am planning to do mitres every other round. I guess I would start with the increases on the round after I pick up the stitches? Thanks in advance to those who respond with helpful information.

You can do increases at the corners, pick up a couple extras there.