There are some problems getting it into the cells (as well as targeting cell-types and specific tissues, as they discuss on the page you linked to), and many diseases are very complex (like cancer), and can't be described by a single causative gene. If you don't have a single gene to target with the miRNA drug, then you can't really create an effective treatment. Other cases (like huntington's, I believe) involve essential proteins which accumulate and cause trouble because of mutations, but are still required to perform their primary function. You can't simply knock out these genes, because you'd be killing the cells that need their function.
As for aids--the reason it's so damn hard to treat is that it mutates incredibly rapidly, so when you target a certain protein or characteristic of the virus with a drug (or in this case, the miRNA you've designed), it's very likely that you're only putting some selective pressure on the virus, and mutants that can evade your drugs will survive and create a resistant population.