The biggest problems with using the clips themselves is that they are very fragile. They can be bent when loading/unloading them, if dropped, even when loading the gun in a hurry. A bent moon clip can tie-up your gun. They are also brass specific. In terms of issues when not using them, the risk of case-under-extractor jams increases and there could be headspacing and reliable ignition concerns.
I honestly don't have a lot of experience myself with moon-clip revolvers, so I'm no subject matter expert, but these were some of the answers I received when asking men like Grant Cunningham, Michael de Bethencourt and Mas Ayoob about them and to me their answers made sense. All recommended avoiding moonclips for defensive purposes. I would give greater credibility to their opinion over that of anonymous posters on Internet gun forums, but that's just me.
I don't know what the likelihood is of experiencing these problems are, but for someone like me who has absolutely no interest in using moonclips, pretty much any increased chance of reliability problems is unacceptable, especially if having to actually pay more money for it.
