Generally these rules will catch 90% of fakes, so you have a very good chance it's genuine at that point.
The other 10% can be caught on small details that involve subtle comparison to genuine coins and known counterfeits.
For example, there are a number of Chinese fakes out on the market now that are made of silver (usually of a lower fineness), so they will pass the silver test; however, these counterfeits can be caught by looking for casting grain on the strike, comparing die pairings, or in some cases counting reeds.
Usually your best bet is to get as many pairs of experienced eyes to take a look at it in those cases. :-)