Pasta – What causes pasta dough to be holey after running through a machine multiple times

Fresh pasta cooks in just a few minutes, so taste it early. It should be al-dente just like properly cooked dried pasta. Let your fresh pasta dry (I hang mine over the back of a chair) for half an hour or longer before you cook it, so that there's some crunch for the al-dente feel.

Most recipes advise "type 00" flour, which is milled extra fine. You should be able to tell when you've kneaded enough - it just needs to feel perfectly smooth in your hands. You don't need to knead for ages like bread dough, but you do need to have mixed the liquid and the flour completely thoroughly.

You're alluding to the correct answer: running it through several times basically kneads the dough and develops gluten.

Gluten provides strength to dough. It forms a flexible, elastic 'net' (the 'net' portion isn't really relevant to pasta dough though) , allowing it to stretch more and is much, much less brittle. Even better, would be to put it through several times, then let it rest for a few minutes so that the gluten relaxes and then continue.

You could also simply knead the dough longer. Many pasta doughs are extremely dry and very difficult to knead by hand - so the kneading mainly happens at the roller stage. If you're using a good mixer or feeling especially hulk-like, then you could knead further by hand.