Most of us miss things as we read. Now that you've read it a few times start studying topics. Pick a subject, say, salvation and read about just that for a month. Or read just a book over and over for a month. Read on the web the history of the book, the timeline, etc.
Meditate on where it was written at and the situations surrounding the writing.
And of course. Always pray for understanding before reading
Good points….the more you read over a certain passage, the clearer the picture becomes and the easier it is to connect passages that support one another. When I study, I pick out main points first and after I have sounded them down, I go back and pick up other details that round out my understanding of the whole passage and even the whole chapter in context. The questions of ‘who, what, when, where, and why’ should always be in the back of your mind as you read and study.
I find too many people who quote verses out of context to back up a belief that the Bible does not teach.
Having a Bible with cross referencing is also very good for scripture to back up other scripture.
I also like to reference interlinear translations and a good Concordance to see how original language words are rendered in other verses. We have to understand that one language translated into another is not as simple as it seems. Phrasing is very different and using the wrong phrasing or punctuation can alter the whole meaning of a verse.
The Bible interprets itself if you just let it….but first you have to eliminate ingrained ideas gained from early indoctrination and let the Bible itself correct them. The Bible never contradicts itself, so if you find a contradiction, it’s time to go and do some research.