Currently I work remotely in the US as a salaried employee for a US company. My wife is considering a job in Norway which will last at least 3 years. Other than the obvious timezone change, what legal, tax, regulatory, etc. considerations do myself and my employer need to take into account?
For this duration, you would need to register in Norway and become a member of Norwegian social security. This would normally also mean that you would need to pay taxes in Norway. As the taxes in Norway are higher than in the US, this does normally imply that you do not need to pay taxes in the US for the duration of your stay.
I think that it would be the easiest to get a residence permit based upon family reunion on the basis of your wife's right to be in the country. Alternatively, you could seek imigration as a skilled worker, register an enkelmannsforetak (a small company) and bill your current employeer for your work. Alternatively, your emloyer could register a subdivision in Norway and employ you directly. Note that this requires your employer to follow Norwegian law with regulations like minimum wage, paid sick leave and a minimum of 21 holidays a year, including National holidays.
You can call Skatteetaten's (tax authority) helpline to find out more about the tax implications. You should get in touch with UDI (immigration authority) to find out if you qualify for family migration which will depend on the type of your wife's visa.
There is one solution that has not been mentioned to be legally employed in Norway, and that is to use a GEO employer of record that is already incorporated locally in Norway and can hire you right away.