A simple system is required:
Concentrate You can't be on the phone, listening to the radio or having a conversation with colleagues and expect to be able to spot errors
Break up the text There are various ways of doing this. You could, for example, break the document into columns and read straight down each column; you could jump around the document reading 'blocks' of text (this is good for checking hard data such as values, quantities etc.); try reading the second half of the line before the first half (tricky, but effective)
Concentrate See above
Don't look for all types of errors at once There are too many types of errors to find them all in one go. Be prepared to scan the document two or even three times to find different sorts of errors. For example: hard data, then grammar, then typos
Concentrate Getting the message?
Finally, skim the full document Having found all, or most of the errors, read through the document, fast, to check that it makes good sense.
And don't forget to c*********e.