Just a couple simple things with your putting since you asked. Question to start though: How much loft is on your putter? The reason I ask is because that can play an important role in how you aim your putter, how much shaft lean you should or shouldn't use, etc. For example, my putter has 2 degrees of loft on it, so I never use any forward press. Matt Kuchar has like 7 degrees of loft on his putter or something like that, and he uses a lot of lean.
Rest the putter head directly behind the ball, not an inch behind it. It appears as if the putter face is aimed right of your target line, so you have to be aware of where the face is pointing. When picking your start line, it really helps to aim at an intermediate target only 2-4 inches in front of your ball, and the face needs to be aimed there. If you aim right -- like it appears you are doing in this video -- then you'll have to make compensations to get it aimed on the line you want the ball to start. Tiger Woods actually does this too, just not as much as you're doing here, so if you putt well doing this, then maybe don't listen to me, but if you're struggling to hit start lines, this is something for you to look at.
Reading the green is critical, speed is critical, stroke is critical, but aiming your putter correctly, is just as critical. When you play, you don't necessarily want to get line-locked and forget about speed, but this is something you should practice and be more aware of.
Secondly, your hands are very much "separate" when gripping the club. Luke Donald here has a more "unified grip," and you can accomplish this in a number of ways. Reverse overlap, double overlap, whatever feels comfortable to you. Unifying the hands more makes it easier to align the forearms correctly (to my knowledge). The triangle formed by your arms would be more symmetrical, and this will affect path.
Again, and I can't stress this enough, but putting is extremely subjective. You don't have to do what Luke is doing here, but it's helpful to be aware of what good players do when they setup and grip the club.
From DTL, you should be aware of where your feet and shoulders are aligned. The feet are aimed right, but the shoulders are aimed slightly left. Try to align those together. I think the feet alignment could be a result of the grip you're using, but I'm not sure.
Again, if you feel you are a great putter, disregard what I'm saying. This stuff is really subjective and people can putt great with all sorts of idiosyncrasies. But I think because of the grip your path seems to be out-to-in. It's a very small arc that we all tend to putt on, but that arc should be slightly inward on the backswing. Perhaps this why it appears you tend to set the putter head slightly right at address.
Lastly, I could be wrong since these are two dimensional images, so take what I'm saying with a grain of salt. I concede I could be wrong on a lot of this, and if so, hopefully someone corrects me.