Is the “Dome of the Rock” the “Abomination of Desolation” spoken of by the prophet Daniel? The Abomination of Desolation spoken of in both Matthew and Mark is specifically in reference to “End Time” perspectives.  Are there any Christian teachings that the Dome of the Rock is the “Abomination of Desolation”?
I'm not sure I'd limit the application "abomination of desolation" to a single event/place/thing.  Many scholars believe that the references in the book of Daniel (Dan. 9:27; 11:31; 12:11) refer to the time of Antiochus IV Ephiphanes who made an unclean sacrifice in the Jewish temple (among other terrible things) in the 2nd century BC.

However, in the New Testament (Matt. 24:15; Mk. 13:14) this would be a past event, so would be applied to something else.  If you look at the parallel passage in Luke you'll find something interesting:


  Mk. 13:14 - "So when you see the abomination of desolation spoken by
  Daniel the prophet, standing where it ought not, then let those who
  are in Judea flee to the mountains."
  
  Lk. 21:20-21 - "But when you see Jerusalem surrounded by armies, then
  know that its desolation is near.  Then let those who are in Judea
  flee to the mountains..."


And then notice Mk. 13:30:


  "Assuredly I say to you, this generation will by no means pass away
  until all these things take place."


So if you take "generation" to mean the people living at that time, then the application here would refer to the time when Jerusalem was surrounded by armies sometime in the first century.  And in fact, we find that the Roman armies did so and destroyed the entire city and temple (70 AD).  The Romans were an abomination that made the city desolate.

Multiple applications seem to make sense because Antiochus IV Epiphanes matches so remarkably well to the descriptions in Daniel, yet Jesus' application had to be different because Antiochus was already past.  They were both abominations of desolation.

Now, as to the "Dome of the Rock" theory.  It is interesting that the Dome of the Rock only exists because the Romans destroyed the temple in 70 AD, so perhaps, in a sense an application of "abomination of desolation" could be made here.

The Scriptures in Daniel and Matthew/Mark/Luke seem to specifically point to the applications I've cited above, but certainly a Jew would view the mosque as "an" abomination of desolation due to its location.