As several people have pointed out Amazon appears to be applying the correct sales tax. The fact that the resident of NJ doesn't understand his own sales tax demonstrates how complex sales tax can be. Every state, county, and city can have their own sales tax laws which have to all be correctly applied based upon arbitrary characteristics. A state can have a tax rate of 4% with an additional 3% for prepared foods and then a city in that state could have a 2% tax on sugary treats. What counts as a prepared food or sugary treat? That will vary just as much and may not even follow common sense, tomatoes have even been legally defined as vegetables for tax reasons.
A national sales tax could make a lot things a lot simpler but would force states to relinquish a lot of power as every business that could use the national sales tax instead of the local taxes would. States with high sales tax would see a large revenue drop while residents of states without a sales tax would be penalized. I could see brick and mortar stores jumping through hoops to selectively use the lower tax rate, if the local tax rate is higher then the national one they'd "order" the item for the customer and then "deliver" it from the backroom.
The best solution I can see is if the federal government runs a sales tax database that every retailer can query. The retailer submits the location, price, item, and some relevant descriptors: "luxury", "food", "service", "book" and the API spits back what the sales tax should be for the item. It's then beholden to the states to keep their relevant data updated. The states would be limited in how creative their sales taxes could be as the software would need to support it but the states wouldn't need to cede power to the federal government.