The January 2011 Tactics Time features a couple of missed opportunities, where the player had a one or two move tactic on the board but did not see it.
How does this happen? One reason is because the person is not looking for it. They might have some plan in mind, or aren’t taking the time to look at the position, and ask themselves the right questions.
Some good questions to ask include:
What pieces are undefended?
How safe is the opponents king?
What checks do I have?
It is also good to see what pieces are lined up.
For example in problem 7 it would be good to notice that the white king is still in the middle of the board. The light square bishop is on the same line as the king, and there is a bishop on that line as well. The dark square bishop is the only thing in the way. Once you realize this, you can see the winning move.
With problem nine, I should have noticed that the rook on h8 is undefended. This would have led me to find the move which wins it.
Of course lots of repetition with tactics problems always helps.
Good luck, and enjoy!