What are the impacts of common pizza dough errors?
I don't see anything in the question that is peculiar to pizza dough. Anything I answer will apply to any kind of yeast-risen, glutenous dough.

The goal with any such dough is a well hydrated protein matrix that has been arranged in sheets that will trap the gas produced by yeast.


If the yeast is dead it won't be able to produce gas and your bread will be somewhere between a cracker and shoe leather- depending on how thick you roll it out.
Using too little yeast is not the same as dead yeast. If you use too little yeast (within reason) they will take a long time to reproduce, eat, and blow up your stretchy proteins. They will be producing a lot of flavor during this period. This will generally taste good.
If you use too much yeast (within reason) the yeast will act very quickly. This is nice for speed but it will result in a much less developed flavor. Neither is a problem so you can choose for yourself.
Using too little water will result in not enough gluten development and a dry, or crumbly dough. The dough won't hold gases and there will also not be enough steam when baking so the dough will be more dense.
Too much water and you have a batter that can't be worked with.
Over working a dough isn't so much of a concern. It is possible to over knead but it is hard to do. See: Possible to over-knead dough?.
Under working the dough will result in less gluten development and very similar results as using too little water- basically you will have unleavened biscuit dough. The exception is if you are following a "no-knead" recipe. In this case the dough is allowed to rest for days which lets the protein sheets form on their own.
Resting the dough is necessary both to relax the protein mesh that you created as well as to allow the yeast a chance to blow it up with some CO2. Not long enough and you won't be able to roll out the dough because it will be too tight and it won't be risen because the yeast haven't eaten. Too long and the bubbles will coalesce into large open cavities. A good rule of thumb is "doubled in volume". Usually about an hour but this is highly dependent on how much yeast you use, how much water, and the ambient temperature.


The end result is that you don't need to worry about most of these things.
The biggest mistakes I see people make is making a dough too dry or simply not kneading enough. It is easier to add flour than water so put in less than the full amount of flour, knead for a while, if the dough stays too sticky then add a bit more flour and knead in.

As answers to other questions have said- you want a dough that is "smooth and elastic" it isn't sticky and looks homogeneous. After just a couple tries you will get a feel for how wet that means and you'll be an expert.

For pizza dough in particular- almost as important as the dough construction is the baking temperature. You want to cook it as hot as you can. 500F in an oven or on a grill. It will only take 5-10 minutes. The fast hot cooking will do a lot for your crust texture. It makes the difference between a crispy, chewy pizza crust and a soft, bready (and soggy under the toppings) crust.