There are definitely problems with using such large unit of measurement (postal codes) for health related/cluster analysis. In laymen's terms the area is too big and you're aggregating up. This doesn't allow for variations that may be present at a smaller scale. If possible you should try to get a finer scale for your data (look into dissemination areas or DE zones). Although, there are many studies that use postal code or even census block information. Please look at studies which use the census so that you can have a better idea of the pros/cons of aggregated data. I can provide these resources at a later time (unfortunately not at home right now should you need them). There is also issues as to how to boundaries are disseminated. How did they choose these arbitrary boundaries? There are other methods which take into account landuse, natural habitat and rivers, etc.
As for having multiple records for a given postal code, you're going to need to do additional statistical analysis so that each postal code is comparing against the same things (ex. by percentage).
If you could update your answer with the specific clustering technique I could definitely try and tailor my answer.
I definitely recommend additional reading on the topic as there are numerous spatial analysis techniques for health related data, especially clusters.
I will definitely try to give a better answer with links when possible, hopefully this will help you out a little!