Anything happens during election can affect the result of election, sometimes quite significantly.
I am concerned about the usage of
sometimes quite significantly
What I want to say express is sometimes it is affected, but not much, but sometimes it can be quite significantly.
Is the sentence above grammatical?
It is not technically incorrect, but it can be refined. I would omit "quite". It is colloquial and overly familiar. "Quite" is conversational English and is OK if you're writing a personal letter, but should be omitted in formal composition.
This stems from a misunderstanding (or very loose interpretation) of the scientific usage of the term 'significant'. With regards to statistics (such as with regards to voting), significant refers to statistically significant, a distinct concept.
The idea of 'sometimes' 'quite' statistically significant is actually rather difficult to justify. It would imply that only sometimes is statistical significance present, and only to a limited degree.
I suspect the writer has no idea this is what she is expressing, and she probably does not understand the concept of statistical significance, but it is instead erroneously trying to use the more common meaning of the term significant (which is more amenable to having a limited degree) where it doesn't belong.
The issue therefore is not really the grammar. It's that in the context the word 'significant' can be assumed to mean statistical significance, and the sentence therefore implies a very weird concept, one of an occasional degree of a mathematical outcome.
Thus we need to re-interpret significant to mean the common usage, which is out of place given the context. With our wider perspective we can now see 'sometimes' and 'quite' are both weasel words. The author is likely using the words to intentionally imply a meaningful statement (that of statistical significance) whilst doing nothing of the sort, since they're using significant to mean something other than statistical significance.
News reports are laden with these weasel words and intentional ambiguities, used by journalists who do not understand the niceties of the subject matter they're discussing but wanting to sound authoritative and as though they have something meaningful to add. It's essentially filler content. It's not grammatically incorrect; it's much worse: meaningless drivel.
To quote Winston Churchhill:
The reserve of modern assertions is sometimes pushed to extremes, in which the fear of being contradicted leads the writer to strip himself of almost all sense and meaning.
...and, further, Theodore Roosevelt:
one of our defects as a nation is a tendency to use what have been called weasel words. [...] If you use a weasel word after another there is nothing left of the other.
This is one of those cases.
