Over-stirring muffin mixtures

The easiest way to tell if you've over stirred muffins, quick breads or cakes is the texture when it's baked.

Correct, and it's all even. Over stirred, and you'll have a series of larger bubbles in the cake, called 'tunneling', where it looks like worms have burrowed their way through your cake or muffin.

Stirring develops gluten, which is essential to trap in bubbles for most yeast breads, and to give it a little bit of chew -- but not something that you want in a typical quick bread. (muffins, cake, etc.)

The main reason behind the claim is that muffins don't want gluten formation. Gluten in a chemical leavened product like a muffin would make it tough, rather than light, since the protein strands are so sturdy. The sturdy structures that are desired in crusty bread are a problem for muffins and other chemical leavened products.

Gluten is formed when dough is heavily mixed or kneaded, or when the dough remains wet for a long period of time. Avoiding mixing it too much is one way of preventing gluten formation.

Lots of mixing can also cause the chemical leavening (baking powder) to go flat. Baking powder is a mix of sodium bicarbonate, which will release CO2 when in contact with an acid, and an acidic salt, such as cream of tartar (or others). They are inert when dry, but when water hits them, the acid activates and starts bubbling the soda. This reaction doesn't take long to run out of steam, though, so too much mixing can pop or shake out the precious bubbles.

What seems to be subject to some superstition is the exact way to get the "right" amount of mixing. Some people say, "ten stirs only" or other little tricks, but the point is that you just want to integrate the ingredients together, and no more, and to add the liquid to the dry ingredients as close to the actual moment of baking as practical. Dry lumps in the batter are fine - they will hydrate quickly in the heat of the oven.

The first claim is true and scientifically correct. If you over mix a muffin batter, in fact any batter or dough containing flour, it will become 'tough' or 'breadier'. This is because in flour (obviously not non-gluten flour) there are gluten molecules (a kind of protein, when the dough/batter is worked the gluten becomes to form strands and microscopic cross-links creating a chewer texture. It will also create a denser texture as chemical leaveners (ie baking soda) cannot rise as well in the tougher batter. Some flours have higher gluten contents, pastry flours have a lower gluten content for more tender baked products such as cakes and pastry, bread flours are produced from hard wheats. And have a higher gluten content and create chewy, breadier product. This links go into more detail:Wikipedia - gluten.

As for leaving the batter lumpy, I've heard this too, however only that it appears lumpy not with pockets of dry flour. I wouldn't advise this as this can result in a muffin with pockets of raw floury just horrible flour. Leaving the flour lumpy but moistened is fine as it means the starch in the flour has moisture to absorb, whilst if undermixed the moisture is unable to reach all of the flour and it stays raw. I don't have a link for this to back it up unfortunately after looking however I've given an opinion from my experience.

Because you have overworked the gluten in the mixture. Same reason why you rest a pastry or pizza dough before you roll it out.

My experience suggests that you can mix a cake batter or a brownie as much as you want, till you are satisfied that all the ingredients are mixed well. The only trick is to not whip the batter or mix it too quickly. Be gentle and your baking powder will work exactly the way it should.