The Mac mini has no problem with high traffic sites. The processor is more than powerful, and up to 16GB of RAM really helps with database lookups. (i.e., mySQL lookups for WordPress). If you have a real active database, you may look into using an SSD drive. They’re quite a bit more expensive, but they tend to be worth it.
When I owned FreeMacWare.com, we were averaging 1.2 million hits per month on our wordpress install. Our Mac mini handled it without a problem.