Each leaf of a lulav consists of two symmetrical halves closed up against one another. The midrib to which the two halves are connected is called a tiyomet.
If the tiyomet of the majority of the lulav leaves are split, it is disqualified. Lechat’hila even part of the leaves should not be split.
Some hold that if the middle leaf was split all the way down, it is disqualified to be used on the first day, because it is considered lacking (this is the opinion of the Rama).
The Sepharadic custom is to perform the mitzvah of lulav by thrusting the lulav forward and then withdrawing it back to one’s chest, as opposed to Ashkenazim who rustle the leaves of the lulav when performing the mitzvah. Therefore, the custom is to choose a lulav that has its leaves firmly attached to the spine, and has the reddish shell around its tip, because there is no need to rustle it. There is no need to remove the reddish shell in order to check if the twin leaves are attached, because we assume that they are connected.
One should be meticulous not to take a lulav where the middle leaf is split and looks like two separate leaves. This halacha applies even for Sepharadim; all the more so for Ashkenazim. But, as we mentioned before, if it has the reddish shell one does not need to take that off in order to check if the leaf beneath it is split.
A person should check the top of the lulav to make sure that the leaf that comes out from the top of the spine is not cut at the top.
If the tip of the lulav spine is bent, it is not kosher for use for the mitzvah. If the spine is straight but the tips of the top leaves are bent, it is kosher because this is a normal occurrence in many lulavim.
One should check the lulav to see that it is straight. One only has to check that it is horizontally straight.
One should check that the spine is at least 40cm long (15¾ inches) and that it is covered with leaves on both sides.
One should be careful not to take a lulav from the tree called Lulav HaCanary (this is a short palm tree with a very thick trunk) since there is an argument among the poskim if this tree is considered “kapot temarim” (which the Torah requires).