Note: I am not a haxe user and would be interested in comments of actual users with respect to the compiler's reliability. My personal conception is that it is quite difficult to define a stable language that defines exactly the same on all targets.
If by reliability you are talking about it consistently not breaking between versions, then it's fine. Between versions the compiler does add new features but for the most part backwards compatibility has been kept between major versions.
If you're talking about does it consistently produce similar code across platforms, then it depends. Plenty of people are using it for 2D games (targetting flash, Android and iOS) and it seems suitable for this. Outside of that, it basically comes down to this: if you want your code to work cross platform, stick to the standard library or to known cross-platform libraries.
As an example, I had a piece of code which took markdown text input, converted it to HTML, and then manipulated the resulting HTML. The code worked on Javascript, Neko and CPP without modifications, because I stuck to existing cross platform libraries.
Compilation speed thing is a "big deal" that I don't hear talked about a lot on HN. Haxe's compiler is so fast that it provides autocompletions by itself. So, completing fields from "using" mixins, constructor inference, structural types, or macro generated methods are all very fast, and guaranteed to be correct. So, perhaps while Haxe's features are not as robust as a few other languages, they feel much more tightly integrated with most coding workflows.
Genuinely interested, I use Haxe and find it's type system advanced enough for me - but maybe there's awesome features in other languages that I don't know about yet.
User should read up on Haxe and may well leave attribution of novelty to correct adjectivation, reads less pedantic in many ways.
Cannese is a really bright programmer though; man built a programming language with an interesting runtime, and manages to use them for his one-man game studio. Not bad.