Once a Presidential pardon has been granted, does the petitioner still have a record, or is the record of the offense destroyed?
Generally speaking, a pardon does not mandate expungement of the record. In United States v. Noonan (Third Circuit, 1990), the recipient of a presidential pardon requested a court order expunging all court records relating to his conviction. The Court ruled that while expungment might be in order when an arrest or conviction was constitutionally infirm, there was no precedent for expungement being granted on the basis of a pardon following an unchallenged or otherwise valid conviction: a pardon did not 'blot out guilt' or restore the offender to a state of innocence in the eye of the law.
This is from the first website that came up in a google search for "presidential pardons" -
http://jurist.law.pitt.edu/pardons.htm - the above answer was under the FAQ section, lots of other interesting info about the history of pardons on there.
ETA: US Dept of Justice - Office of the Pardon Attorney (includes application process) -
http://www.usdoj.gov/pardon/index.html