I would like to present a fundamental machlokes about בורר which will hopefully give people new insight into the melacha of בורר. Note, this post does not go into any questions relating to practical halacha.
The Baal Hamaor in Perek Haoreg writes that even though in general a מלאכה שאין צריכה לגופה is פטור, בורר is an exception because the definition of the melacha of בורר is taking פסולת from אכל which is a מלאכה שאין צריכה לגופה and therefore the general principle of מלאכה שאין צריכה לגופה is פטור doesn't apply to בורר.
The Ramban in Shabbos ק"ו: disagrees and claims that בורר is a מלאכה שצריכה לגופה.
What is the machlokes?
It would seem that the machlokes is what did the Torah prohibit when it prohibited בורר? Did it prohibit the action (selection) or the result (making the food better like the melacha of cooking)?
The Baal Hamaor holds that the melacha of בורר is the action of selection. This is why he calls it a מלאכה שאין צריכה לגופה because the thing that you are doing the melacha on, the פסולת you don't want.
The Ramban on the other hand holds that בורר is a prohibition of making the food better (purifying it), therefore it is a מלאכה שצריכה לגופה as the melacha relates to the food which you want.
There are a number of very important נפקא מינא based on this. I will mention 2 here.
1. Is there a prohibition of Borer where the items are clearly separate distinct items (e.g. socks)?
The אור שמח states that the prohibition of בורר doesn't apply where the items are separate items even if they are mixed up. The only time there is an issur of בורר is where the 2 things blend into 1. A good example is chulent, all the different components blend in and it is 1 chulent, to pick out the beans would be בורר. However, socks are clearly identifiable items and therefore there is no בורר.
The other poskim disagree with the אור שמח and hold that there is בורר in this case as well.
The machlokes could be this machlokes. The אור שמח understands בורר like the Ramban, the issur is to make the food better. By clearly identifiable distinct items like socks, there is no תיקון. If I have blue socks and black socks mixed up, if I take out all the black socks I have not improved the blue socks in any way shape or form. The blue socks remain the same old blue socks that were there before I took out the black socks. Since the issur of בורר is to improve the food here there is no בורר as I have not improved the blue socks. Only in something like chulent, where if I take out the thing I don't like I have improved the chulent is there בורר.
The other poskim hold like the Baal Hamaor that the issur is the act of selecting. Therefore there is no difference between socks and chulent.
2. If the פסולת is more then the אכל can you take out the פסולת? Tosafos say no, since the פסולת is greater taking out the אכל is the normal way of בורר. The Ramban disagrees and always allows you to take out the אכל.
This also can be explained based on the above. Tosafos hold like the Baal Hamaor, the action of selecting is prohibited, therefore where the normal way is to take the food that is prohibited. The Ramban is לשיטתו that the issur is making the food better. Therefore you can always just select the food.
This is clearly a fundamental machlokes and needs to be applied to all of hilchos בורר. The 2 נ"מ that I listed are just the tip of the iceberg.