If you replace "a surprisingly large proportion of mistakes" with "many mistakes" then it may be easier to see "mistakes" is plural.

Alessandra, I know that my answer is a little late, but when I found your question today it was very intriguing to me. Logically you are absolutely right that the verb agreement in your sentence should be singular, but as a native English speaker I knew that the singular in this context did not sound correct. On investigation I found that there was a strange (to me anyway) difference to the verb agreement depending upon whether the definite article (the) or indefinite article (a) is used in the noun phrase. For example: In your sentence the indefinite article (a) is used and, even though the subject (the noun phrase “proportion of mistakes”) is singular, the verb is plural in agreement with the plural noun (“mistakes”). This would also be the case if the noun is singular, but refers to more than one person (e.g. crowd, group, team etc.). However if your sentence had started with the definite article (the) then the verb would have been singular as you suggest (i.e. it would have read “The surprisingly large proportion of mistakes seems to have its origins ...”). There does not appear to be much logic about this usage, but I suppose that is why the English language is so fascinating and difficult to master.

no. it is correct as it is. mistakes is plural. even if portion is singular, you are still referring to a collection of mistakes