From the New Republic, reprinted today on Media Matters:

Far from being a mark of exemplar service, the honorable discharge is better
thought of as a standard severance, something every soldier receives unless
there's significant evidence of misconduct and a commanding officer eager to
brave the paperwork, panels, and disciplinary hearings required to send the
soldier home with anything less. Like any number of other officers, Bush could
have ducked out of his service for months and still received an honorable
discharge.

Going missing from military service and then squeaking out with an honorable
discharge has a rich history among politicians. Current U.S. Representative
Bobby Rush, a Democrat from Illinois, served in the army through the mid-1960s,
becoming progressively more involved with radical antiwar groups. In 1968,
after Martin Luther King's assassination, he went AWOL from his unit to help
found the Illinois chapter of the Black Panthers. Weeks later, he was honorably
discharged.

In 1999, a Texas sheriff up for reelection saw his candidacy unravel after
local newspapers reported that, despite a subsequent honorable discharge, he'd
skipped out on Army service for several months in 1976 to "patch things up with
his ex-wife."

AND

A few years ago, a guest columnist for the St. Louis Post-Dispatch ruminated on
going AWOL from his unit routinely with a "case of beer" to drink himself "into
oblivion." "I don't know how, but I did manage to get an honorable discharge."

AND

Perhaps more striking is how often serious questions of misconduct have been
flat-out ignored. John Allen Muhammad, convicted last November for his
participation in the D.C. sniper shootings, served in the Louisiana National
Guard from 1978-1985, where he faced two summary courts-martial. In 1983, he
was charged with striking an officer, stealing a tape measure, and going AWOL.
Sentenced to seven days in the brig, he received an honorable discharge in
1985.