The comic[1] that I posted in the previous thread has a nice overview about the situation.
The specific issue the EFF article is pointing out is how the ISDS is designed to trumps national sovereignty, so business can strong-arm countries into removing any law they don't like.
It works more or less like this:
1) pass TPP as a treaty, which by definition has the same power as a constitutional amendment. (this is probably a serious bug in the constitution). This means TPP trums congress.
2) TPP sets up an international tribunal (ISDS) that hears complaints from businesses. (i.e. "Australia is hurting our tobacco sales with their plain packaging laws"[2])
3) The tribunal, as mentioned in this article, would be staffed by, "three private-sector attorneys who take turns being the judge and the corporate advocate." This conflict of interest would be a serious violation of ethics requirements in most legal systems.
4) The tribunal rules that your local law violates some foreign requirement, as determined by the ISDS and their business-assigned judges, and the local legislature is forced to repeal the law. ("Australia's plain packaging laws is seizing the trademarks of Philip Moriss, in violation of a 1993 trade agreement if we carefully abuse the agreement's language")
That's the short version, and I'm leaving out some details, of course. It should work as a decent overview of ISDS is a threat to national sovereignty.
[1] http://economixcomix.com/home/tpp/
[2] this example is covered well by John Oliver: https://www.youtube.com/watch?v=6UsHHOCH4q8
edit: oops.. s/ISPS/ISDS/