It would depend on what you're trying to treat. Based on the condition, you can see if the theory behind it makes any sense, and then there's the matter of whether it works in practice, and how good the practitioner is. I understand that in classical homeopathy only one remedy is chosen to fit the person's constitution and such, the practitioner does a detailed intake to try and figure that out.
One thing that I find significant is that I have been told by a health care professional (not one that actively practices homeopathy, just someone who knows about it, though they're not against it) that a homeopath will withhold certain information from you in terms of what they think you're like, your constitution etc. indicating a belief that your opinion of their assessment of you will have an impact on the results. Now we know about the placebo effect, but whether it's perceived or real change, if the mind makes a difference why not work with that? If it doesn't, then this wouldn't be necessary.
So it seems to me this points to the role of the mind, which is something I think is important. Frankly on a behavioral level we know that bad habits in your lifestyle can create chronic problems of different types, and a lot can be changed if you can change those behaviors. We can also talk about stress, yet another function of the mind, so there's a lot that you can impact there. But what it comes down to is the individual rather than a substance or something external.
Homeopathic "remedies" are usually harmless, but their associated misbeliefs are not. When people are healthy, it may not matter what they believe. But when serious illness strikes, false beliefs can lead to disaster.
Well, if there's not a molecule of the stuff left the remedy itself can't do any harm, and considering the remedies really cost very little money isn't really an issue as far as the stuff itself is concerned. What is an issue is failure to seek other treatment, which the author here fails to explicitly state. Beliefs have to do with the believer, not the stuff you use. If you want to spend a few bucks on the side just to see if it works it's probably not going to do any harm, but common sense dictates that you consider all treatment options if you don't want to or can't afford to use yourself as a guinea pig. For some people, especially those who've exhausted conventional treatment options, they can't afford NOT to seek alternatives if it is a serious illness. Naturally you'll want to make an educated decision in all cases, but I tend to agree with the guy that said "to regard our ignorance as knowledge, this is mental sickness."