How far off can your percent error be to still be considered accurate

5% would be good, but more or less may be acceptable if the measurements are easy or difficult.
I would consult past papers on the specific subject you are studying.

http://apps.webofknowledge.com

It depends on the margin of error determined for the exercise. There is no general universally prescribed margin of error

some places its 0% you ahve to be highly acurate
others may give you a leeway