A cut leaf:
Tiyomes: Lechatchilah, if the Tiyomes leaf was even partially cut at its top it should not be used. If however no other Lulav is available, then if its majority length is still intact, it may be used with a blessing. If majority of it has been cut, it is invalid according to all opinions. [Thus one is to avoid buying a Lulav with a very pointy top as it is easily possible for this point to break and invalidate the Lulav for initial use.]
Remaining leaves: If the remaining leaves of a Lulav, other than the Tiyomes have been cut at their top, it remains Kosher.
What is the law if the cut of the Tiyomes is only noticeable after close examination?
It is valid, as the invalidation of Hadar is only applicable if viewable at first sight.
Many Lulavim grow a needle like wooden point at the top of the Tiyomes. If this area is cut off is the Lulav Kosher?
The Lulav remains Kosher as this area is not considered part of the actual Lulav.
Admur brings a dispute in this matter: The first opinion rules that if even a small amount of the middle leaf, the Tiyomes, was cut off it is invalid, as it is no longer considered Hadar. The second opinion rules it is only invalid if majority of the Tiyomes has not been cut off. [ibid]
 The reason: As it is no longer considered Hadar. [ibid]
 Rav A.L. Cohen
 So is implied from Admur as rules Rama 645; However the Michaber rules that if the top leaves are cut off [not specifically the Tiyomes] the Lulav is invalid.
 Piskeiy Teshuvos 645/9
 Kashrus Daled Minim p. 91; Ikarei Hadaat 33/23; Piskeiy Teshuvos 645/12