I'm mainly interested in opinions on the trade-offs between having a single central server all the websites connect to as opposed to each website mirroring a subset of the master database with all the products in it. For example, will I run into severe performance issues (or even security issues, or restrictions) making queries to an offsite database? Will we hit scalability issues we can't handle early on from the sheer bandwidth required to maintain this? If we do go with something like a script that keeps smaller databases (each containing a subset of the central master data) in sync, what sorts of issues will we likely encounter there? I would really like the opinions of people far more knowledgeable than I am regarding the pros and cons of both setups and what headaches we are likely to encounter.
CLARIFICATION: This should not be viewed as a question about whether we should implement one database vs multiple databases. This question has been answered numerous times. The question is regarding the pros and cons for a deployment like this having the ability to manage all the websites centrally (one server) vs trying to keep them all in sync if they each have their own db (multiple servers).
REAL-WORLD EXAMPLE: We are a t-shirt company, and we have individual websites for our different kinds of t-shirts, but we're looking at a central order management integrated with our single shopping cart (which is ColdFusion + MySQL). Now, let's say we have a t-shirt that's on 10 of our websites and we change an image for it. Ideally we would change that in one place and the change would propagate, but how would we set this up?