I am tackling phenomenology but the qualitative reliability and validity are quite similar to case study. You have added advantage of triangulation. Be sure to clarify reliability from validity as reliability is necessary but not sufficent for validity. In Qualitative research you may wish to move to the nomenclature of Lincoln & Guba (1985). These sources will get you started:
Morse, J. A., Barrett, M., Mayan, M., Olson, K., & Spiers, J. (2008). Verification strategies for establishing reliability and validity in qualitative research. International Journal of Qualitative Methods, 1(2), 13 – 22. Retrieved from http://ejournals.library.ualberta.ca/index.php/IJQM/index
Onwuegbuzie, A. J., Leech, N. L., Slate, J. R., Stark, M., Sharma, B., Frels, R., … Combs, J. P. (2012). An exemplar for teaching and learning qualitative research. Qualitative Research, 17(1), 16–77. Retrieved from http://www.nova.edu/ssss/QR/
Meyrick, J. (2006). What is good qualitative research? A first step towards a comprehensive approach to judging rigour/quality. Journal of Health Psychology, 11, 799-808. doi:10.1177/1359105306066643
I agree with Gail, the above sources are a good start to get you thinking about rigour/reliability in non-positivist methods of enquiry, an area that I find is both important and very interesting. Here are some other articles that might be of use:
Stige, B., Malterud, K., & Midtgarden, T. (2009). Toward an Agenda for Evaluation of Qualitative Research. Qualitative Health Research, 19(10), 1504–1516.
Finlay, L. (2002). Negotiating the swamp: the opportunity and challenge of reflexivity in research practice. Qualitative Research, 2(2), 209-230.
Finlay, L. (2002). ''Outing'' the Researcher: The Provenance, Process, and Practice of Reflexivity. Qualitative Health Research, 12(4), 531-545.