ESL Podcast 1196 has sentence like
I want you to verify the facts and figures and to flag anything.
Could someone describe the difference between "to flag" and "to mark"?
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If you are to mark something, you write or put something (a note, a symbol, or some formatting that would make the 'marked' thing/object distinguishable from others).
A flag is a type of mark. But, in essence, it creates the impression that there is something important. The logic behind this is, when one literally raises a flag, it readily/easily grabs people's attention.
So, based on the sentence, 'you' will flag those that caught 'your' attention. (probably factual errors or inconsistencies that will also catch the attention of other people who'll see the flags thereafter.) - the usage here is similar with 'mark'.
To me, "to flag" has an implication that the item is being marked as having some problem, while "to mark" does not have that implication: it might be for a problem, but it might be for other reasons.