Jim,
Thanks for that video. So far, I've watched it about a dozen times. One thing I did notice was that you still do a little pulling backwards. Muscle memory. Issac mentioned starting on the near side for dovetail cuts - that way one can follow both lines at the same time. I find that for the far corner it's easier to use the toe end of the saw and for the near corner it's easier to use the heel end. That's for back saws. Big rip saws are another ball game whose rules I have yet to comprehend let alone master.
In my quest to learn the use of a hand saw I have tried many approaches. For dovetail cuts where any lack of precision tells I have found Kevin Glen-Drake's Kerf Starter to be a very useful tool. A properly sharpened and burnished Kerf Starter leaves a nice guide trench for the saw. They come is different plate widths so you can match to your saw's plate. I have yet to try using it for dado cuts. One day - RSN.