http://youtu.be/7VPKspiZAoc http://youtu.be/FT9epQlDa5M http://youtu.be/jMjaoiLNNmA Somewhere there is a good description(better than I could write) of how to cut knee braces on a compound mitre saw but I'm can't seem to find the link.
There are many others. There are many different styles and joints in timber framing. Choose the ones that are appropriate for the use and are easy to cut with the tools you use. I use different joints when cutting with a chainsaw compared to when cutting with a skill saw for example.
It is the end product that is important. There are many approaches to getting to the end product. Even inside a shop there may be two or more different approaches to reaching the same product.
As a general rule power tools are often used to get close to a line and hand tools are used to finish to the line.
A tenon is a good example. Depending on the wood grain I will cut the shoulder with a circular saw then finish the depth with a hand saw and knock away all the excess with an axe or a chisel and mallet. Or if the grain full of knots or going in a bad direction I will make relief cuts out from the shoulder to the end of the tenon just shy of the edge of the tenon to assist the removal of wood. I've also taken the saw and cut in from the end. It may even depend on my mood on a particular day.
On mortises I do the same relief cuts as a tenon and clean with a chisel or slick, just cut the mortise first, it gives the base of the mortiser/boring machine somewhere to sit.
In short the only wrong ways are ways that either don't work or aren't safe. Some ways are more efficient than others but that depends on your comfort level and tool selection.
I've heard rumours that German apprentices at some point needed to finish cutting a tenon in 5 minutes using only an axe. Maybe I don't have the right axe.
