I see that both phrases "**in light of**" and "**in the light of**" are used and people considering both to be correct. Look [here][1] and [here][2]. Also there is a large corpus supporting both phrases usages; you can consult [here][3].

Question #1:
>Though both seems to be correct in terms of being used in writings, which one is grammatically correct? 

Question #2:
>In there any difference in their meaning implications?


  [1]: http://www.usingenglish.com/forum/threads/125665-in-light-of-or-in-the-light-of
  [2]: http://forum.wordreference.com/showthread.php?t=2718896
  [3]: http://corpus.byu.edu/glowbe/