I use 1/16 precision, and occasionally find that a dimension is off 1/64 or even 1/128 but it is rare. In the architectural field, if you use anything less than 1/4" on your drawing as cab stated, they will look at your plans and laugh at you....
The 1/16 precision I use is to make sure the drawing I have is correctly drawn, and exactly drawn...not just drawn "good enough"
Personally I would recommend against tracing over drawings, but if you do, I would recommend that you trace them to a close tolerance using the snap grid set to a precision you feel comfortable with. At least this way, if the original line is 3 43/128, you can have it snap to 3 1/4, 3 3/8, 3 5/16 or whatver degree of precision you want.