Can a staff member tape a series of TV programs for class?

Yes, as long as you are copying programs for educational purposes on behalf of the educational institution, the New Statutory Licence allows you to copy anything broadcast on TV or radio, including Australian pay TV services.

The copy should be marked with the appropriate Copyright label and then becomes the property of the institution. The University Library is the most appropriate home for these copies.

Have you considered using a streamed version of the TV series?
The University Library subscribes to EduTV (a multidisciplinary streaming video database providing access to documentaries, series and drama from various free-to-air and pay TV channels.)