Since this summer, I've been working hard on my left and right hand synchronization. I spend some focused time on it every day, and I try to give it at least subconscious attention in all areas of my playing.
I see this as the most important aspect of my technique. The nuances of the attack, intentional or not, help define a player's signature sound across all types of guitars, amps, and effects. The more control I have over mine, the closer I get to the sound I'm going for, and the better I understand what that sound is.
My ultimate ideal note attack works like this. Starting with my right hand, I want to avoid all unintentional noise, which usually means no picking mistakes. Next, I want to minimize the sharp, scratchy sound of pick on string, especially on strings already in motion from previous pluckage. This takes some practice on its own; quickly strike through the string with the tip of the pick without resting the pick against it or sliding across it. (When I get a chance, I want to experiment with rubber and felt picks. I'm curious to see how much pick noise they reduce, and whether it's worth getting eraser shavings all over my pickguard.)
This quick pick attack gives the left hand a small window in which to work. Unless I'm intentionally cutting off notes early, I want notes to be separated only by the pick attack. When playing a new note, at least one finger needs to fret or release a note. During that tiny moment when my finger is touching the string but not quite fretting the note, this creates excess noise.
The key is to cover up the left hand's movement with the right hand's pick attack. Say you play a C followed by a D on the same string. The C note should be stopped not by lifting the finger fretting it or by the new finger ready to fret the D note, but by the pick, in the process of picking the D note. The new finger for the D note shouldn't touch the string until after the pick does, and it needs to be fully depressed, properly fretting the note, before the pick leaves the string. The same goes for switching strings. That tiny fret noise of releasing your finger from a fretted note won't be heard if it's in perfect sync with the pick attack.
In short, all the action of changing to a new note with the left hand should occur while the pick is touching the string, in the process of picking the new note. Keep in mind that I advocate a very short pick attack, so this time frame seems impossibly tiny. I honestly don't expect to achieve perfection on this. But thinking about it this way gives me a precise goal to pursue. It doesn't need to be perfect to sound good; the closer I get, the better it sounds. My hands and ears have already shown great improvements from the focused attention, and I'll eventually reach a point where my ears can't tell the difference anymore.