There are several interesting details about the find. DNA tests showed that the man had both Hansen's disease and tuberculosis. When the Bible uses the word "leprosy," is is using the generic term for a wide range of skin diseases, and does not necessarily refer to Hansen's disease - but this man had Hansen's disease.
The leper's shroud was in two pieces - one for the head, and one for the body. This matches the burial practice for both Lazarus (John 11:44) and Jesus (John 20:5-6). This gives another reason to doubt the genuineness of the Shroud of Turin (the supposed burial cloth of Jesus), since it was a single cloth, not separate head and body cloths.
The leper's shroud was a simple weave of wool and linen. Although some scholars are pointing out that this is another difference from the Shroud of Turin, my first thought was wondering why they used an unkosher cloth. Mixing any two kinds of cloth was forbidden in the Torah (Lev 19:19), and a linen-wool weave was specifically forbidden (Deut 22:11).
The picture: a diagram of the "Shroud Tomb" showing where the remains and shroud were found.