If I want to say I just quickly check a paragraph of text and didn't find typo, but the checking is quick and not careful or thorough. What is a good verb for that?
I would suggest Cursorily. It means Performed with haste and scant attention to detail
For a verb, consider skim
to read (a book) in a superficial or cursory manner
I can't think of a single verb that adequately says all that you wrote in your original question. If you were expected to check for typos, I suggest saying it explicitly to avoid assumptions on the part of the person you're addressing: "I scanned the paragraph and didn't see any typos." (More formally: "I took a cursory look at the paragraph and didn't notice any typos.")
See a definition of "scan" here: http://dictionary.reference.com/browse/scan?s=t (I'm new to this site and didn't post the definition for IP reasons; please let me know if this is a problem.)