You should be able to set up the server scheduled script to perform a find for all records with today's day of the week name selected in that check box field.
Enter Find Mode 
Set Field [YourTable::Yourcheckboxfield ; DayName ( Get ( CurrentWeek ) ) ]
Set Error Capture [on]
Perform Find 
I'm not quite sure I understand, is there a "IS Checked" type of function? I figured out how to create the checkboxes, how to use them/script around them is the problem at hand. Although you may have just answered it, I am still in the fog, apologies.
A check box formatted field enters the text shown into the specified field each time you select a check box and deletes it each time the check box is cleared. When you select several check boxes, the text for each is entered into the field, in the order the check boxes where clicked, separated by returns.
You may find it informative, to make a copy of your check box field on your layout, put it next to the original copy and reformat it as an Edit box. Then click different checkboxes and note what text is actually stored in the field.
So the above script, when run on a Monday, will only find records where "Monday" is a word entered into the check box field and thus should find all records where the Monday check box has been checked.