According to a brochure I received at the IRS Forum, there were over 77.1 million return filed on paper last year (tax year 2003). Of those, 5.9% had errors which had to be corrected before a refund could be processed. In the same time period, there were 48.5 million returns e-filed and the error rate was .07%.
When you e-file, the computers involved check your math, verify all the SSNs and names, and rule out other major preparation errors. You know within a few hours if there are any problems and can correct the return. When the return is mailed in, you do not know for weeks if there is a problem. Usually, the first sign of trouble is when your refund does not show up when you expect it.
There are other good reasons to e-file but the best is catching any mistakes early.