There are a set of bill/notes that are automatically presumed to be counterfeit. Banks, currency exchange shops don't take them, no matter what.
Before you go abroad, remember to do the following
1. bring newer notes, (new series) - it is assume that there a lag for the counterfeiter to "catch up" with the new design.
2. bring newer/less circulated notes - if it is not torn, or overly used, it is freshly off the press
3. bring higher currency notes, 100, 50, not 20's or smaller. Usually a better exchange rate is offered for larger notes, (it typically doesn't apply to banks, only the individual shops)
4. Avoid these series of notes
For 100's
CB leading serial numbers
For 20's