I don't know what your problem is. I'd have thought it had something to do with your browser or system abilities with dmg files. You could try Jum's beta builds. But these are betas. No installation necessary. Just drag & drop the program from the mounted dmg. It might be an idea to stop it mounting automatically after downlding. Then mount manually. According to Stief, Firefox is also safe to use for dmg files. You might want to check out the OS X version of it. (F.F. doesn't run well on my system which is why I don't normally recommend it.)
http://www.mager.org/LimeWire/