I believe that a common problem for people who are proof reading documents is the brains tendency to complete patterns based on partial information. This causes a person to read not what is actually written but instead what they expect to read.
For example, if you had seen the cliched sentence "The cat sat on the mat" tens of times over your lifetime then you might tend to skim ahead and miss the mistake in "The cat sat on the met."
One approach to reduce this problem is to consciously direct your attention in such a way as to reduce your own expectations. Some common tactics include:
1. Take a break in between writing the text and editing it. The common advice for writing essays in school is to leave your draft shut up in a drawer for a few days before returning to it.
2. Examine each word in the text in a way which separates it from the context of the sentence it is written in. You could do this by physically pointing at each word with a finger/pen as you read it, or by reading the text backwards from the last word to the first.
The above might increase your ability to spot a spelling mistake but will do little to assist whole-sentence grammatical mistakes. My best advice for that task is to read the text out loud. I find it much easier to hear such a mistake than to see it.
For the problems with reading you might wish to do some research on "active reading". Reading with a question in mind can help you to properly concentrate on the material.
The question might relate to a specific piece of information, eg skimming through a tutorial to discover "What arguments does the make_widget command take?"
The question could also be focused on the structure of the text, eg "What is the main idea of this paragraph?", "How could I rewrite this complicated sentence in my own words?", or "How does the evidence introduced in this paragraph relate to the claim stated at the beginning of the chapter?"