I sometimes miss very obvious moves. How can I improve my game? I am a hobby player but I would like to improve my game. 

I like to watch annotated games. For instance, I have watched all games of Josh Waitzkin in Chessmaster GM Edition.

Also, I watch games in YouTube as well.

In some variations, I find so said "hard to find" or "advanced" combinations at a glance. The correct move almost shines on the board.
In some other variations, on the other hand, I really struggle to find a simple mate-in-one move or a beginner's fork.

What would be the reason behind this behavior of my brain? How can I improve my vision?
I think you should do more Tactics training (https://www.chess.com/tactics/) (http://chesstempo.com/chess-tactics.html). Also You should read this

Here's an important segment


  There are a few common targets that will help you in finding tactical targets in chess:
  
  1-   Hanging (undefended) pieces can be used to gain tempo moves or to win them in tactical combinations.
  
  2-    An exposed (unsafe) king is a permanent target that can easily be combined with other threats.
  
  3-    The geometrical relation between pieces, in example – pieces on the same diagonal, file or rank.
  
  4-    A piece with a very important defensive task can become a target for an attack.
  
  5-    A piece with more than once defensive task can become overloaded and exploited.
  
  6-    Pieces in attacking positions versus pieces in defending positions have more flexibility and thus more opportunity for tactical maneuvers.
  
  7-    A majority of forces in a certain part of the board can outnumber the defenders and create opportunities for a tactics.
  
  8-    A piece with severely limited mobility can sometimes be trapped or kept out of the game.