Anytime you do a URL formula which edits or adds a record, you need to the redirect to display a record or a report as the next action, or else the API not so subtly reports its success or failure back to you.
If you want to next reDisplay the Original Record, and for some reason you want to use the aPI method, it would be like
var text URLONE = the code you had above ending in semicolon;
var text URLTWO =
URLRoot()& "db/" &Dbid()& "?a=API_EditRecord" &
"&rid=" & [Record ID#]&
"&_fid_42=1";
var text URLTHREE = urlroot() & "db/" & dbid() & "?a=dr&rid=" & totext([Record ID#]);
$URLONE
& "&rdr=" & urlencode($URLTWO)
& URLENCODE ("&rdr=" & urlencode( $URLTHREE))
