A signed applet can do pretty much anything an executable app can do if the user gives it permission. I built a little zip utility applet years ago that accesses the file system, ezyzip.com. Still works even though the signature is expired.
Wow, I hadn't noticed that about Java before, Just checked ezyzip.com. The sig is expired, but it only says that right at the bottom of the dialogue, and it still allows you to run it without a problem. I can imagine many people just clicking through that, as it seems almost identical to the standard Java applet warning.
Oracle really need to change that, there should be flashing red lights (alright, maybe not flashing) on that dialogue, otherwise any previously valid signature on a Java applet will be happily trusted by the majority of the internet.
Also, I noticed that in the comments on the bitcointalk site, that many people are blaming this on windows. I know the payload is an EXE, but has anyone analysed it and checked if this applies to other OS's as well? If this is (as the author claims) a Java 0-day attack it may well work on other operating systems, and for other purposes. I personally suspect this is a matter of the author accidentally granting permissions to an app that he shouldn't have, but it sounds like this "AdobeUpdate-Setup1.84.exe" could do with some analysis.