James, there is really no wrong way to twist wire, unless you do a horrible job at it. There is a bout 10 different ways I can think of to connect the wires together before the solder goes on so saying thats wrong is like saying you are breathing wrong. While yours may not be the way most goes about it, it isn't coming apart because of the solder so you are fine.
The solder is fine, it is actually soaked through the wire good, and every exposed bit has been covered. The solder isn't just clumped up on top of the wire so its okay.
-Steven-