Do Mormons believe that all spirits are omnipresent? Are all spirits omnipresent? According to Mormon doctrine, God is omnipresent through his spirit, does that mean that all spirits are omnipresent or is the Holy Ghost a special case?
LDS commentary on this question is sparse, but based on the below information I infer that the answer is no.


  “The Holy Ghost as a personage of Spirit can no more be omnipresent in
  person than can the Father or the Son, but by his intelligence, his
  knowledge, his power and influence, over and through the laws of
  nature, he is and can be omnipresent throughout all the works of God
  (Joseph F. Smith, Gospel Doctrine, 61)


In other words, presence is related to knowledge, power, and influence over and through the laws of nature. These are areas where other spirits are deficient.


  Each spirit child of Heavenly Father differs in intelligence. Jesus
  Christ is more intelligent than all of Heavenly Father’s spirit
  children, and His wisdom excels them all. The Pearl of Great Price: Teacher Manual, (2000), 44–46


Because other spirits don't have the perfect intelligence, knowledge, power, and influence of the Holy Ghost, they probably can't have omnipresence either.