Shortcrust done in the food processor is easy and quick and yes it all can be done right in the processor. However, when you put the butter, flour and salt in the processor to process, make sure you only process the dough to look like rough breadcrumb texture. Then while the processor is running slowly add some cold water in the funnel until the dough JUST comes together. (only add enough water to bind the ingredients together, nothing more. The shortcrust should be a little rough when taking out of the predecessor, wrapping in plastic wrap and setting in fridge to chill before you use it.
Shortcrust traditionally is done with the rubbing in method with the fat. You would rub the butter in with the flour and salt until it looked like breadcrumbs. Then add small amounts of cold water to barely incorporate the ingredients together.
You want to use cold ingredients and chill the dough before rolling out or working with it as it warms up really quickly. It should roll out nice and smooth without overworking the pastry.