I am inputting direction-distance information into the traverse window. I enter a distance, but when I see the line it doesn't match up where it should with other layers and when I measure it with the measure tool it is not the same distance that I entered into the traverse window.
you wouldn't have been using a Web Mercator coordinate system would you?
if so, you shouldn't do measurements on maps using it, unless you know that the distances are corrected... which they usually aren't