Do you mean that making a graph using a temperature proxy measurement, tree rings, then switching to recorded temperatures only at the point they diverge rapidly, without mentioning this change, is proper?
Actually, it was mentioned in the notes immediately below the graph in the IPCC report where that was done.
Is it also proper to use one specific type of tree as the basis of the graph, if that one type is the least likely to show historic temperature changes?
Well according to the paper in question, they used 12 proxies, of which 9 were various tree-based proxies and 3 are ice-core based proxies.
Wouldn't it be better to use results from trees that more accurately show historic temperature changes?
As previously noted, 9 different tree proxies were used and they were likely the best available proxies at the time. It's not like we all have 2000 year old trees lying around in our backyards.
This improper normalization procedure tends to emphasize any data that do have the hockey stick shape, and to suppress all data that do not. To demonstrate this effect, McIntyre and McKitrick created some meaningless test data that had, on average, no trends. This method of generating random data is called Monte Carlo analysis, after the famous casino, and it is widely used in statistical analysis to test procedures. When McIntyre and McKitrick fed these random data into the Mann procedure, out popped a hockey stick shape!
You might want to read this explanation of the events your mention. To make a long story short, McIntyre and McKitrick made critical mistakes that exaggerated their findings (which were published in a social science journal that doesn't do peer review). Subsequent hockey stick graphs have been generated using the same data with different methods, different data with the same methods and different data with different methods.