If most the upper leaves of a lulav were pared or truncated, or the central leaf is pared or truncated, the lulav is invalid for use on the first Yom Tov (SA and Rema 645:6). If there is a thorn-like protrusion on the tip of the uppermost leaf, it is not considered part of the lulav, so even if it is singed or cut off, the lulav is kosher even according to the most meticulous.
A lulav whose uppermost leaf ends in a zigzag, as sometimes happens, is kosher le-khatḥila.
If most of a lulav’s leaves have dried out and turned white, with no green left at all, the lulav is invalid (SA 645:5).
The spine of a lulav must be at least 4 tefaḥim tall (c. 32 cm, or 25.3 cm in pressing circumstances). This is the minimum size required to fulfill the obligation. However, it is a hidur for the lulav to be tall, as is accepted (MA 672:3).
In recent times a question has arisen concerning the validity of lulavim from a particular species of date palm imported from the Canary Islands. The Canary Island date palm differs from the common date palm in several respects: its leaves are shorter, denser, and softer; it is greener, and its dates do not taste good; its spine is softer and more flexible, bending in whichever direction it is tilted.
Those who deem the Canary Island date palm acceptable maintain that since it comes from a palm tree that produces dates, it is kosher, despite all the differences (Tzitz Eliezer 8:22; R. Shlomo Zalman Auerbach). Others say that since its dates are not so edible and it differs from the common date palm in so many ways, it does not qualify as the “branches of palm trees” referred to in the verse (Igrot Moshe, OḤ 4:123). In practice, since there are acceptable species of the date palm similar to the Canary Island date palm, the reasoning of those who are lenient seems more convincing. Nevertheless, since this is the subject of dispute, it is preferable to avoid using a lulav from a Canary Island date palm. When circumstances are pressing, one may rely on those who are lenient, use it, and recite the berakha.