One big mistake I see on the greens is that golfers' backstrokes are too long. Why? Well, it's an ugly cycle. First, they tend to decelerate the putter into impact, which leads to a lot of putts left short. After they see a few weak ones, they think they need more juice, so they make an even longer backstroke. Soon, they're making these long strokes with nothing on them at impact.
Also, the longer the backstroke, the harder it is to stay aggressive and square the face at impact. All short-game swings, whether with a wedge or a putter, should have a symmetry to them: back and through the same amount. That makes it easier to apply the hit and control the distance.