Tilting the hand slighly so that the back of it faces outward a bit is definitely something almost EVERYONE fucks up.
The rest, which your link doesn't say, is that the portion of the arm from shoulder to elbow should be perfectly parallel to the ground, and from the elbow to the fingertips the arm should be at a 45 degree angle.
If the elbow is slouching, or the hand is not facing outward a bit, it's a really ugly salute, and to me, is not only lazy but disrespectful.
Paulie, when I went through Basic Military Training, one of the first things I learned is that military personnel can and do salute differently, especially--in a negative context--when the forearm and elbow are perfect, but the hand is bent and looks horrible or the palm is noticeable. This tends to be what I see from time-to-time.
My salute, when I bring my fist across my midsection, have my palm straight and facing towards me, and have my middle finger in the appropriate location, tends to have a slight sagging in my elbow. I've practiced it quite a bit, and that's just how it is.... As with many things in Basic Military Training, my MTI (Military Training Instructor) would correct it once, and then after realizing that that is just how my elbow was, would leave it alone. The same would go for other MTIs as well...
When I graduated, I was a bit self-conscious about it, and when I brought it up to my father (who served years ago), he also remarked that many of the military personnel--including the MTIs--had different saluting styles, and that I shouldn't overanalyze it. Officers would just appreciate the sentiment.
To this day, when I salute an officer, I have not been corrected, nor have I been accused of being "lazy" or "disrespectful," which I most certainly am NOT.
In the future, I hope you will remember this before you ignorantly judge another military member as being "lazy" or "disrespectful" for having a slightly sagging elbow. I noticed that you did not critique the Master Sergeant/E-7 next to President Bush for having a slightly sagging elbow. When you are in full service dress, try to touch your elbow to your back.... when the tailor laughs at you for being an idiot and ripping your uniform, remember this post. Thanks....