"...each marking is supposed to represent 5/1000's of a degree."
As a surveyor, I was constantly dealing with error; something that is always there in even the most precision instruments available. So, the first thing to do is accept that you'll never get it perfect.
On surveying instruments, bubbles are generally used for rough leveling, and other mechanisms are used to increase the precision. Without knowing the particulars of the level you used, I have my doubts that it can be read accurately at that level of precision. Rotating your bubble level is the sort of method that is used by surveyors in order to eliminate as much error as possible, so you have done what you can within the limits of the tool you're using.
Now, the question remains; if you have a measurement you can trust, is 10/1000's of a degree something to worry about? In the span of a foot, it amounts to a difference of about 2/1000's of an inch; a little less than the thickness of a standard sheet of printer paper.
As a surveyor, I was constantly dealing with error; something that is always there in even the most precision instruments available. So, the first thing to do is accept that you'll never get it perfect.
On surveying instruments, bubbles are generally used for rough leveling, and other mechanisms are used to increase the precision. Without knowing the particulars of the level you used, I have my doubts that it can be read accurately at that level of precision. Rotating your bubble level is the sort of method that is used by surveyors in order to eliminate as much error as possible, so you have done what you can within the limits of the tool you're using.
Now, the question remains; if you have a measurement you can trust, is 10/1000's of a degree something to worry about? In the span of a foot, it amounts to a difference of about 2/1000's of an inch; a little less than the thickness of a standard sheet of printer paper.