There are also different treatments of capital gains, and phantom gains which arise only from shifts in exchange rates. For anyone of any means beyond their salary alone these both can lead to paying more combined tax to both countries than either would require individually. Thats dual taxation in my book.
Phantom gains have been particularly bad in the last decade with the falling US dollar. In Australia, house prices in my area about doubled between 2002 and 2012, but with the change in exchange rates, the IRS calculates the gain as if the price had more than quadrupled!