In find mode use " " in a specific field to search for a null value, or to constrain your found set.
That works in find mode in the layout, but when I tried to use "" in the script editor, it insists that "" doesn't match the date format. I was able, however (in "try any random thing before I rip out my last grey hair" mode) try the asterisk in the criteria box and it works to constrain the found set by omitting the returned DDRs! My script is tamed. Now I have to wonder what the "zero or more characters" definition of the asterisk means. Isn't a null field equivalent to zero characters? Thanks, your suggestion got me moving in the right direction.
I use "" in scripted finds frequently with FileMaker 11 and don't get any such error message in the script editor. So, I'm suprised you got that error message. (We used to see that error with set field and date fields many versions ago, but don't in recent versions.)
Using "" will fail to find the records you want, however, if the field where you enter it, is from a related table where there may not be a related record. In those cases, * with omit works when "" does not.