Perhaps in response to US court saying "the Australian court lacked jurisdiction over EFF", the Australian court will say that the US court has no jurisdiction in Australia. The Australian court could conceivably force the EFF to change how its site is shown to people in Australia. Then after realizing that people in Australia can still access the US version of the EFF's site, force the EFF to change its site in all countries.
This sort of problem could become more common, such as the case that Google lost where the Canadian Supreme Court ruled that Google had to remove results in violation of Canadian law from all Google results worldwide.