I don't see how that could happen on a new installation. It checks if the column is there and if it isn't adds it. You can run this query though:
ALTER TABLE mybb_threads ADD moved INT UNSIGNED NOT NULL DEFAULT 0;
Thanks, after run command, work fine.
Installed this today. Attempting to search just seems to refresh the search page. Search parameters populate in the URL and seem to be accurate, but the search doesn't actually run. The search page just reloads with /search.php?action=do_search&keywords=test&postthread=1&author=&matchusername=1&forums%5B%5D=all&findthreadst=1&numreplies=&postdate=0&pddir=1&sortby=lastpost&sortordr=desc&showresults=threads&visible=&submit=Search in the URL.
myBB ver 1.8.23 + latest build of Fast Search.