Mogen clamp is commonly used for Jewish circumcision (brit milah). Other methods for baby circumcision are Gomco clamp circumcision and forceps guided circumcision. In my experience, these methods are not superior to Circumplast or Plastibell circumcision in newborn circumcision.
The complications specific to Mogen clamp circumcision include injury to the glans if it is not below the inferior edge of the clamp, and an asymmetric incomplete circumcision due to malpositioning of the clamp (typically more redundancy ventrally).
Reference: Complications of Circumcision: TheScientificWorldJOURNAL (2011) 11, 2458–2468 ISSN 1537-744X; doi:10.1100/2011/373829)