What gets confusing for some of us non-Europeans is that we assume finely ground "00" flour is probably low-protein (like our finely-ground cake and pastry flour). In fact, the protein content of "00" flour can range quite a bit depending on what kind of wheat it's ground from. Most "00" flour that we see in the United States is ground from durum wheat and has a mid-range protein content of about 11-12%, similar to all-purpose white flour.
Besides the level of the grind, the other big difference between "00" flour and all-purpose flour is how the gluten in each flour behaves. The gluten from durum wheat flour tends to be strong but not very elastic, while the gluten in red wheat flour is both strong and elastic. This means that with durum wheat, we'll get a nice bite on our breads and pasta, but not as much chew.
All this said, it's generally fine to substitute all-purpose flour for "00" flour. You'll notice a texture difference if you grew up in Europe or are very familiar with with products made from "00" flour, but all your recipes will still come out just fine.
Do you think "00" is necessary when making authentic Italian foods? Do you notice a difference when using it?