In this context, it means "pay close attention to."
To "note" can mean "to notice," "to pay close attention to, and to remember."
Examples of use:
"Now, watch closely, and take note of exactly how he places his feet before jumping."
"Don't listen too much to what he says, but do take note of what he does."
Here, it means that Barnum tried to observe and understand Maelzel's techniques. It means that Barnum was trying to learn by taking Maelzel as a model. It does not mean that Maelzel was personally giving Barnum advice or teaching him.