If mail works with the -f parameter set on then that is better.
By default, sendmail won't let you change the "envelope address" of the email, that is the return address, so you often end up with nobody@your.server.name instead of a useful mail address.
This can harm you in the eyes of spam checks, though the -f param doesn't always work (it definitely doesn't work with safe_mode).
With -f, you can set that to an arbitrary email, which is better for spam and lets you actually control where bounce/delivery errors go.