What can make a shofar non-kosher (i.e. halachically unfit)?
A shofar must be at least one tefach (9.6 cm) long, not including the mouthpiece.
Cutting off the end of the shofar or reducing the thickness of the shofar walls does not render the shofar invalid, as long as it retains the minimum length.
Shofars of any pitch are kosher, as long as the sound of the shofar has not been artificially modified (e.g. by adding to it).
No substance or coating may be added to the mouthpiece. The remaining part of the shofar may be coated on the outside, as long as the coating does not alter the sound the shofar produces.
The shofar must be fully intact, without any holes. Under certain circumstances a shofar with a hole may be used � assuming it was not patched, which would alter the sound.
Ideally a shofar should be free of any cracks. In the case of cracks that run along the length of the shofar, if no other shofar is available (e.g. a crack is discovered on Rosh Hashana and there is no kosher shofar nearby), one can rely on the opinion that the shofar remains kosher as long as the crack does not extend along the majority of the shofar’s length (or if it does extend along most of the length, the crack has been glued).
In the case of a hairline crack, the shofar may be used even if another shofar is available, but even so the crack should be fixed before Rosh Hashana so that the shofar does not appear defective.
In the case of a crack that runs along the width of the shofar, if the crack extends along the majority of the diameter, the shofar is pasul (unfit) and should not be used on Rosh Hashana, etc. If the crack does not extend along most of the shofar’s diameter the opinions vay and a qualified rabbi familiar with the halacha should be consulted.
This article is based on Chayei Adam, Hilchot Rosh Hashana, Klal 140.