One of the most famous Halachic questions to come out of New Zealand (and Japan) is the question of where the Halachic dateline is.
Briefly the question is where the dateline should be. The International Dateline marked on maps is loosely based on 180 degrees from Greenwich. Given that Halacha doesn’t (necessarily) recognize Greenwich as the center of the Earth, there doesn’t seem to be reason for Halacha to accept the arbitrary dateline in common usage today.
There are various Halachic opinions as to where the halachic dateline should be, most famously the Chazon Ish who moves the dateline West of its current location, making Shabbat on Sunday in New Zealand and Japan. Rav Tucazinsky moves the dateline East, which would make Shabbat on a Friday in Hawaii. (For further background to the issue, see this article by the Star K.)
A lot of people have trouble understanding the question, because they think of the dateline as something that is fixed and universally accepted. How can there be a question whether a day is Friday or Saturday. To put the question in perspective, you should realize that historically there have been many changes to the dateline, and in fact there will be another adjustment this week.
The South Pacific Islands of Samoa and Tokelau have decided that they should be on the Western Side of the Dateline to make their time zone more similar to their closest neighbours and major trading partners, New Zealand and Australia.
This means that on these Islands, Thursday December 29 was followed by Saturday December 31.
As far as I am aware, there are no Jewish Communities on these Islands, but the Jewish Virtual Library estimates 100 Jews in Oceania outside New Zealand and Australia. If any of these Jews are in Samoa or Tokelau, they would be faced with an enormous Halachic issue.
Assuming that until now any Jews in Samoa followed the opinion of the Tucazinsky, and kept Shabbat on Saturday, seven days after last Shabbat will be Sunday January 1st, which according to Tucazinsky should be Shabbat.
It would be difficult to justify keeping Shabbat on Saturday one week, and then keeping the following Saturday which is only six days later, based on an arbitrary decision of the government to modify their time zone.
If anyone has a Halachic solution for the Jews of Samoa and Tokelau, feel free to leave a comment.