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SUMMARY
1. There is a dispute about how to make a house with a roof of boards into a valid Sukah.
2. There is a dispute about whether an equal amount of closed space and open space constitutes a private domain on Shabbos.
3. If metal rods are put on top of a Sukah, and then valid Sechach the size of a rod is placed between every two rods, the Sukah is valid.
4. One may not use scraps of vessels for Sechach.
5. There is no proof from our Mishnah for the law above (#4).
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A BIT MORE
1. Rebbi Yehudah: This is the subject of an argument between Beis Shamai and Beis Hillel. Rebbi Meir: One must take a board out and place a piece of regular Sechach in its place in order for it to be a valid Sukah.
2. Rav Papa: If it is exactly equal, it is considered a Reshus ha'Yachid and one is permitted to carry within this domain. Rav Huna brei d'Rav Yehoshua: It is not considered a Reshus ha'Yachid.
3. According to Rav Huna brei d'Rav Yehoshua (#2), the amount of space taken up by the Sechach must be slightly more than the amount of space taken up by the rods.
4. They seemingly fit the description of not being able to become Tamei and having grown from the ground. Nevertheless, the Rabanan decreed that they are unfit since they were once part of a vessel that could have become Tamei.
5. Even though our Mishnah teaches that planks from a bed may not be used as Sechach, perhaps it is referring to a long plank from the side of the bed when it is still attached to the shorter sides of the bed and has some utility (and therefore is still a vessel in some regard which can become Tamei). It might not be referring to a lone plank.
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