I have been through all the tax settings several times now, without finding any solution to this problem.
When looking at the shopping cart, the subtotal is displayed with incl. tax, and is correctly calculated from the items in the cart. The Grand total has a value that is the same as the Subtotal excl tax, and if I choose to show Grand total both incl and excl tax, the Grand total excl will correctly be calculated excl of tax of the value of Grant total incl, tax, which as I said before, shows a value being equal to subtotal excl tax.
There are now shipping or discounts in the picture, so subtotal should be the same as the Grand total. The setup is done for Norway, so the VAT is 25 %.