My definitioon of a "serious collector" is anyone who systematically acquires coins for a collection and knowledge about coins. Acquiring knowlege is nearly automatic if a collector is following a collection. Some people might not though and no matter how much money you spend if you aren't learning then you aren't a serious collector. A few "investors" should be considered "serious collectors" since to some extent acquiring coins one believes will increase in price is a sort of collection and many actually do learn something about the market or coins.
I think it's a state of mind and it takes place once the person gets past the "I want" buying everything in sight / buying it because it's popular phases. If he can get past that and still have an interest in the hobby and collects, he's serious.