A lot has changed since the 2004 Presidential election. Many states that initially embraced paperless, electronic voting systems have replaced those systems with paper ballots, or have added printers to electronic voting machines that produce a voter-verified paper audit trail (VVPAT) of electronic ballots.
Paper ballots and VVPATS are important tools for verifying the vote, and many states have enacted automatic, post-election manual audit laws that require paper ballots or VVPATS be used to verify the accuracy of computer vote counts. This is accomplished by hand-counting a sample of paper ballots or VVPATs and comparing the hand-counted tallies to computer vote counts.
Manual audits of election results are important because, while most states allow candidates to request a recount, actually doing so can be expensive and politically unpopular. Automatic manual audits of election results means those results will be verified regardless of the election outcome or whether a recount is sought.