I'm in Washington State. When entering in my 1099-INT info, I uncheck the "My form has info in other boxes" but it doesn't save and always says "needs review".

There is no Individual state income taxes in Washington. You can skip the state input screens.  I would recommend deleting the 1099-INT in TurboTax and then re-entering it.  Go to Search at the top of the screen then enter Form 1099-INT in the search box.  You will see a Jump To function that will take you to the 1099-INT input screens.  Click the trash can next to the 1099-INT to delete it.  Re-enter the 1099-INT.   Unless there are amounts in any other boxes other than box 1 or box 3, I would not check the My form has info in other boxes

Nine states — Alaska, Florida, Nevada, New Hampshire, South Dakota, Tennessee, Texas, Washington and Wyoming — have no income taxes. Tennessee and New Hampshire, however, tax interest and dividends, although Tennessee is phasing out its tax in 2021

Seems like the problem was when Turbotax tried to auto fill in the info straight from my bank. I ended up removing the 1099-INT from my wages, entered it manually and then it worked.