(Mishnah): A stolen or dry Hadas (myrtle branch) is invalid.

If it was worshipped as an idol or from a city that must be destroyed (due to the idol worship that exists there), it is invalid.

If the top is cut, the leaves are split, or there are more berries than leaves, it is invalid.

If he reduced the number of berries it is valid, but this may not be done on Yom Tov.

(Gemara): The Pasuk states (Vayikra 23, 40), "and the branch of the "braided" tree" - where the branches cover most of it and a "braid" runs along the branch. The Pasuk is referring to a Hadas (myrtle).

If you suggest that it is the olive branch, it does have a braid but its branches do not cover most of it.

If you suggest that it is the 'Zargonah', its branches cover most of it but it does not have a braid. (Only the Hadas tree has both of these characteristics.)

Chiya bar Ada quoting R"SBL: When the Mishnah said that more berries than leaves is invalid, it is referring to black berries. (When berries begin to dry out they turn black, but when they are still moist they are green, which does not disqualify the Hadas.)

Question: Why do black berries disqualify the Hadas? Is it because they do not look like the branch or is it because the berry has ripened and the Torah requires a branch rather than a fruit?

Answer: A practical difference between these reasons is if the branch grows green berries. If the problem with black berries is that they do not look like the branch, green berries also do not look like the branch, so it is invalid. Alternatively, if the reason is that the Torah requires a branch but not a fruit, and since green berries are not yet considered fruit, it is valid.

(Mishnah): A stolen or dry Aravah (willow branch) is invalid.

If it was worshipped as an idol or from a city that must be destroyed (due to the idol worship that exists there), it is invalid.

If the top is cut, the leaves are split or if it is a Tzaftzafah, it is invalid.

If it is withered, if most of the leaves had fallen off or if it grew in a field (rather than next to a river), it is valid.

(Gemara - Beraisa): The Pasuk states (Vayikra 23, 40), "and Aravos of the river".

This Pasuk seems to only allow those that grew next to a river; from where do we learn that even if it grew in a field or in the mountains it is valid? The Pasuk states "Arvei" (plural) - even Aravos of other places are valid.

Aba Shaul says - "Arvei Nachal" teaches that there are two Aravos, one for the Lulav and one for the Temple.

If so, why does the verse mention a river? To exclude a Tzaftzafah.

What is a Tzaftzafah? If its appearance is like a serrated sickle (where all of the blades face one side and bend towards the handle), it is invalid. If its appearance is like a serrated knife (where each blade is double-edged), it is valid.

What is a invalid Aravah? If its leaf is round and its stem is white. What is a valid Aravah? If its leaf is long and its stem is red.