I came for a visa interview yesterday and I was given a Form 221(g) and was asked to bring some additional details or was told that my case was pending for administrative processing. The same form says I can reappear without making another appointment on certain days of the week. I would like to know how long this letter is valid for me to reappear for another interview without an appointment.
You are advised to follow instructions as given by the Officer at the time of interview. You may re-appear when you are ready with the required documents within one year from the date of your original application. After that date, you would need to make a new appointment and pay the required application fee again. (There's a time slot reserved for such cases and vary from consulate to consulate. Check with the applicable consulate for the timings.)
 
If the officer has checked the box that the case is pending for administrative processing, then the applicant will need to wait for further instructions from the Consulate about completion of his or her case. In many instances, the delay is due to some further processing, i.e. name checking or fingerprint check, and may take several weeks to resolve. Applicants will be notified as soon as the processing is complete and whether the visa can then be approved.