I find the attendance module is extremely useful. I use it in all the classes I teach with Moodle. The only thing, I believe, would make this module more effective is to add time element for example:
A class meets every Monday at 3 pm. for 2 hours in a computer lab or online then any student login to the class at 3 pm. and will be attended automatically, if s/he logout then the time s/he stayed online will be the period s/he was attending the course; therefore will be graded according that time.
If a student login later than the time of the class his attendance will be stamped with, lets say, Tardy for
If a student login after the classs time is over s/he will be Absent.
This will make the attendance and its grading much accurate.