[gcrump]

Thanks very much, that did work, figured out to the state is checked. Now I would like to then set the style of that row to use the strikeout attribute... I attempted (see comment) but no luck....

tell application "OmniOutliner Professional"
tell front document
repeat with theRow in (every row whose state is checked)
-- change "done" to the name of your done column
set theDate to value of cell "Done" of theRow
if theDate is missing value then
if (value of cell "Due Date" of theRow is not missing value) then
set value of cell "Done" of theRow to "today"
-- change "due" to the name of the due column
set value of cell "Due Date" of theRow to missing value
--- change to strikeout attribute
--- set style of theRow to bold
end if
end if
end repeat
end tell
end tell