I was thinking, should we require answerers to provide some source for their statements or ask to make it clear when the answer is based on net research and not on any canon resource?
I think we should have a policy similar to that on scifi.stackeschange.
Basically, each answer should, of course, be based on something, even if the answer is an original research. That may be references to particular anime episodes/manga chapters, references to profile wikis or other Internet sites, references to official statements and interviews of the authors, and so on and so forth.
What should you do if you see an answer that doesn't have any references? First of all, if you feel the answer is speculative, or may be misleading or even wrong, leave a comment to kindly ask it's author to include references to the sources of the information. If you want, you may give it a preventive down-vote, but if you do, for heaven's sake, don't forget about it, re-check the answer later and remove the down-vote if the issue is fixed! I've seen many examples of people forgetting to remove their down-voted after the post is fixed. It is very frustrating for the author. It has happened to me a couple of times on stack overflow: my post was misunderstood and down-voted, I fixed it to be more clear, then the post had numerous up-votes/was accepted, but the down-voters never reversed their votes because they just didn't bother to check the post again after some time.
Of course, if an answer is wrong or misleading, the author ignores the requests for sources or infringes some copyright, or anything else, you can feel free to down-vote the post, or vote to delete it, provided you have enough reputation for that.