The most common P’sul in a Sukkah is for people who put up the walls after they put up the Schach. People put up the frame of the Sukkah then put the Schach and then put up the walls. When the Schach are put up the walls are not yet complete. That is the P’sul of Ta’aseh V’loi Min Ha’asui. The Schach must be put up when it is already a Kosher Sukkah. It is a P’sul even B’di’eved.
Can a Goy put up the Schach on the Sukkah? In Maseches Sukkah it says a Sukkas Ganvach, meaning a Sukkah of a Goy is Kosher. So at least B’di’eved it Takeh is Kosher. However, there is a Biyur Halachah in Hilchois Tzitzis in Siman 14. He lists there all the areas where a Goy L’chatchila can’t do things. One of the areas is building the Sukkah which means putting up the Schach.
In Taf Reish Lamed Beis S’if Beis it says if there is some airspace between the Schach it wouldn’t Pasul the Sukkah. However, in the event where the airspace runs the whole length of the Sukkah, no matter how large or small the Sukkah is, the Mishna B’rurah says that is a P’sul in the Sukkah. So don’t sit under that portion of the Sukkah. The Sukkah itself would be Kosher if there are 3 other walls that are Kosher. Anshei Ma’aseh are careful that if there is bamboo across one way of the Sukkah, and there is nothing going across the other way, they will put some bamboo the other way as well. Or at least put a board in the opposite direction. With a Schach mat you don’t have such a problem, because the string that attaches the mat together is Mafsik the airspace.
If someone puts up Schach on a rainy day and has a covering over the whole Sukkah during that time, in most cases that Pasuls B’di’eved. This is another case of Ta’aseh V’loi Min Ha’asui.
According to every Poisek besides for the Chazon Ish, there is never a P’sul B’di’eved on the type of material used to support the Schach. If you want to be Yoitzei the L’chatchila, support the Schach with a 2 by 4 of wood.
Why do people when they check over an Esrog take off their glasses? There are 2 issues that come up with an Esrog. One is the issue of Shinui Mareh. This is a discoloration. Something that is the wrong color is only a P’sul if you can see it from a distance. If you can only see it by taking off your glasses and looking closely there is no P’sul of Shinui Mareh.
If it can be seen from a distance the Halachah is a bit more complicated. On the top of the Esrog it Pasuls in one spot. On the rest of the Esrog besides for the Choitem (top) it Pasuls only if it is on both sides of the Esrog.
Sometimes a tiny dot can be a Chosher. A Chosher is when part of the Esrog is missing. Chosher is a P’sul on the first day of Sukkos. This year that we are not an Esrog on the first day of Sukkos, so Chosher is not a P’sul this year. Sometimes an Esrog becomes a Chosher because of the thorns that are on the Esrog tree, or sometimes the trees are sprayed and in the strong morning rays of the sun which are magnified and it makes a burn hole in the Esrog. You can tell a burn hole because it is symmetrical on all sides because it came from a droplet of liquid. It does not have to be perfectly round.
How is it possible to have a Sukkah that is Pasul and by adding Pasul Schach you make it Kosher? If you have airspace that Pasuls the Sukkah, which is 3 Tefachim. Schach Pasul only Pasuls if it is 4 Tefachim. So if you put the Schach Pasul there it will make the Sukkah Kosher.
How is it possible to have a Sukkah that is Kosher and by adding more walls you make it Pasul? The Minchas Chinuch has a situation of when you add wall you make the Sukkah Pasul. There is a Toisafois in Sukkah Daf Tes, who asks why do we need a Gizeirois Hakasuv that Sukkah Ta’aseh L’cha and not a stolen Sukkah, it is a Mitzvah Haba Min Aveirah anyway? If you have a Kosher Sukkah with the minimum amount of 3 walls, and one of the walls has a space of air of less than 3 Tefachim. The smallest a wall can be is 7 Tefachim, so there are now about 4 Tefachim and a Mashe Hu. We are now using Lavud to make it a Kosher Sukkah. If each person takes a stolen piece of board and places it in the space to complete the 7 Tefachim, it makes the Sukkah Pasul even though the Sukkah was Kosher before. Now there is no Lavud, however, 3 Tefachim of it is made out of Sukkah Gezulah which is not Sukkah Ta’aseh L’cha. It is not a Mitzvah Haba Min Aveira because without this 3 tefachim of wall the Sukkah would have been Kosher. It is only Pasul because of Sukkah Ta’aseh L’cha.