The primary issues in that book were 'what can a character know' and 'what will a character do'.
So what can a character know? For the sake of simplicity, I will use 'he' here, but in reality, it applies to either gender.
When you create a character, it doesn't matter the age, from maybe six to a hundred and sixty, he will start out with what you put in his head. He might be a genius and he might be an imbecile, he might even be a savant of some sort, but after you make your character whatever he is, he is a closed cell. After that, he is restricted to what he can perceive through the senses you gave him, generally sight, hearing, touch, smell, and taste, for the most part, in that order.
After his personal senses have been explored to their limit, his next option is to search out answers. This is generally what carries the story along. The ways a character can go after information is pretty much infinite, if you ask me, but it can also be accidental.
The issue with the before mentioned book was that the kidnapped father seemed to know that his daughter would be looking for him so he left her clues, clues only she would be able to find. This premise is fine by itself. It's just how it was handled. First, the daughter didn't bother to even start searching until the last minute. Second, it seemed as if the father was leaving clues where he couldn't, leaving information he wouldn't have the time to assemble, not to mention leaving information he couldn't possibly know at the time. Ahhh I'm getting way to close to another rant. Let me get back on track. The father couldn't possibly have known where his boat was going to be hidden, and if he did, if he was there (possible), would he have taken the time to create the clue containing the name and number of the attacking ship while his crew and friends were being murdered?
This question brings us to the second issue. What will a character do? Your characters make logical decisions all the time. Anything from whether or not to pick up a pen to which direction to walk to what color shirt to wear. Logically, a lost character who knows where people are will head in that direction. A lost character who does not know where people are could head off in any direction, but in reality, they would weigh the possibilities before picking a direction. It might be as simple as heading downhill or picking a direction by the sun.
For a person to stumble upon information, there needs to be a feasible reason for him to be in the same location as said information, and there needs to be a logical reason for that information to be there in the first place.
For me, logic is very important when it comes to what people decide to do. Logic can come in variety as uncountable as there are people, but it's still logical within that character. Stress can make a person make choices that are less than logical, but the theory is that your reader will know about the stress, and can digest the choice. The personality of your character can also affect the choices he makes - one reason why it is important to have a variety of personalities within your story.
Back to the story. Of all the people on this earth, the father was leaving clues for one person capable of deciphering them, and yet the only reason she found the clue that set her on the track was idle curiosity in a case she should never have been exposed to. I also didn't get the sense that she was an avid diver since she hired the man to be her guide, therefore there was no better reason for her to come across the information necessary to carry forward the story. With key changes in this one character, many loose ends would have been smoothed over.
So, what can your character know, and what will your character do? Keep it all logical, people.