OK, after watching the video, that is steel, not bronze or a brass alloy that I first mentioned because of the color.
What appears to be rust on the OD of the workpiece may indicate stock that was left out in the weather for a while. Some materials "age" a bit when exposed to the elements for extended periods of time.
It looks like you are experiencing hard spots in the workpiece which is aggravating the harmonics of the operation. Something appears to be loose, either in the headstock, carriage or compound. Take another cut and try laying your finger against the carriage where it contacts the ways to see if you can detect any movement. Repeat with the compound and compound rest. Of course, do this AWAY from the workpiece.