For this error:
Invalid SQL:
SELECT * FROM reviews_reviews WHERE active=1 AND status=1 AND logo<>'' ORDER BY postdate DESC LIMIT 5;
I suspect it was during the uninstall/install process and a bot hit the page, and triggered the error, I would not worry about it. Cause obviously the table is there, as you are able to add reviews.
What happens if you edit the feed, and click on the Preview Feed button?