The walls of the sukkah must be 40 inches (10 tephachim) tall, and a sukkah requires at least three (kosher) walls. Those walls must be reasonably rigid, and if they flap too much in the wind then they are not acceptable.
There must be enough schach on the sukkah to cover at least 50% of the sukkah, thereby creating a situation where there is more “shade” (covered area) than “sun” (uncovered area). If there is an area in the middle or on the side of the sukkah where there is absolutely no covering for 10 inches (3 tephachim), and that “empty” area runs from one end of the sukkah to the other, the entire sukkah may well be non-kosher. This sometimes occurs when there are strong winds and some of the schach mats get blown out of their original positions. If a Mashgiach suspects that his store’s sukkah may have this type of large “open” area, he should either add schach or ask a Rabbi to look at the sukkah and render a decision.
L’chatchilah, the shach should not be nailed or tied down to the sukkah with a material that is not suitable as schach. In order to prevent the schach from moving around or blowing off during Succos, it is advisable to place a large 2X4 across the top of the schach (perpendicular to the schach) to hold it in place.
If there is an area in the sukkah which is covered by an overhang, tree, or other covering which is not suitable for schach, then the sukkah is kosher as long as that covering is not wider than about 7 feet (4 amos). That said, the area which is underneath overhang etc. is not considered a kosher part of the sukkah, and a carefully worded sign should be put up indicating this.
It is acceptable for non-Jews to build the walls of the sukkah and to place the schach on top of those walls. However, a sukkah is not kosher unless the walls are put up before the schach is placed on top, and therefore a Mashgiach or other knowledgable Jewish person must oversee the building of the sukkah to ensure that this requirement is followed. Although we assume that a sukkah put up by a local shul or community organization is kosher and acceptable for use, the cRc takes direct responsibility for all sukkah’s located at certified establishments, and they should therefore be inspected and approved by Rabbi Eisenbach or Rabbi Katz before Yom Tov.