By the post title, I don't mean philosophical problems, so much as practical ones.
First, and most telling, is the problem of definition. "Everything is natural" could be the simplest definition of metaphysical naturalism. To pin things down though, what does "natural" even mean here? Without having a clear definition, natural cannot be distinguished from alleged supernatural stuff, let alone claimed as all which exists.
Surprising though it may seem, I have often seen metaphysical naturalism asserted with no definition at all. This was not, admittedly, by philosophers, but self-declared metaphysical naturalists nonetheless. Asking for definitions, in my experience resulted only in insults or logical fallacies as responses.
Such fallacies I've seen to support it were begging the question and shifting the burden of proof, e.g. "You know it's true!" or "Prove the supernatural!" Well, clearly many people do not "know" it, and the person who asserts this has the burden. They do not accept replies like this from supernaturalists-why should anybody when the same has come from them?
Since atheists are generally metaphysical naturalists (some even regarding them as basically identical), this also leads into a weird contradiction among those who assert atheism is merely "lack of belief". Holding a metaphysical naturalist view is a positive assertion though, which if true logically entails (as not only atheists but theists agree) there is no God as generally defined.
Positive atheism would be justified in that case-i.e. God does not exist, rather than simply being unproven as they often assert. Yet they seem unaware of the conflict from what I've seen, or at least will not state this logical conclusion aloud
I must reluctantly conclude that two explanations can be given for this. One, they are unable to support their metaphysical naturalism, so despite asserting it they fall back on negative atheism. Two, it is easier to just claim the supernaturalist/theist has the burden of proof, then critique whatever evidence they offer.
Both, of course, could also be in play. This however is a contemptible cop-out to me. Atheist philosophers of course have supported positive atheism by and large, plus metaphysical naturalism. So those I'm referring to here are the "Internet atheists" (who ironically often express a disdain of philosophy).
Similarly to the above, methodological naturalism has many of the same problems. It's often asserted that science cannot examine supernatural claims as they are not empirical, which is in fact nonsense. Putting aside once again the definition issue, claims of the supernatural are frequently empirical ones.
Certainly, some of these aren't, either due to vagueness or other issues. However, many are, and have been tested in the past. Thus the methodical naturalist assertion seen so often here seems like another cop out, and most likely done to avoid conflict. Yet that does not save them-the fundamentalist is not fooled.
All this is not to say that I think metaphysical naturalism cannot in fact be defined or defended. Carrier's definition here I think is at least a good attempt at one. He also makes similar points about methodological naturalism. It's the Internet atheists who are vexing on these topics.
