Sometimes I wonder why it took me so long to understand the importance of keeping the bow on the same place on the string during the duration of a given note. I always knew about the importance of keeping my bow straight, but I always (abstractly) thought of the sound of a note as being connected with the caprices of the bow hair, and not with the actual vibration of the string. Two bouts of forearm tendinitis, and loads and loads of frustration has finally given way to a simple realization that I would like to share.
I find that if I keep my attention on the actual sounding point, and think of the trajectory of the bow as secondary, while I "observe" the vibration of the string, it is much easier to control the sound. Bow changes become incidental and brief interruptions of the string's vibration (and once in a while they don't interrupt the vibration of the string at all). It is really easy to inadvertently allow the bow to slide to another sounding point when the left hand changes position. Consciously avoiding this tendency, and keeping the bow on the sounding point during a shift, allows the string to remain vibrating, and makes for a better-sounding shift. It works with any sounding point--even one near the bridge or near the fingerboard. It makes harmonics far easier.
When I share this with my students, their playing gets better instantly. They begin (as I have begun) to lose tolerance for any deviation or dullness in the sound. I wonder why none of the people who acted as my teachers ever noticed my problem? Perhaps it was one of those cart before the horse things, and I was quite expert at hiding it--especially from myself.
I explained this graphically to one of my recorder students (a person who doesn't play the violin) over a cup of tea. I held a knife in my right hand (like a bow), and I held a spoon in my left hand. I Tried to keep the knife connected with the same spot on the spoon by controlling the knife from its handle. The I tried keeping the knife connected with the same spot on the spoon by focusing all my attention on the spot on the spoon, and letting the knife make its own path. The second way, which involves much less effort, is far more effective. Trying this without equipment, using only the index finger of each hand, is rather enlightening.
Just a note on equipment. I only noticed this AFTER I got new bridges on both my violin and my viola (after 15 years).