Anki does not currently have a bug bounty program, but if you have discovered a security issue, a private message on our support site would be greatly appreciated. No account is required to post a message:
https://anki.tenderapp.com/discussion/new
Anki allows users and shared deck authors to augment their card designs with Javascript. This is used frequently, so disabling Javascript by default would likely break a lot of the shared decks out there. That said, the default may be changed in the future.
The computer version has a limited interface between Javascript and the parts of Anki outside of the webview, so arbitrary code execution outside of the webview should not be possible.
AnkiWeb hosts its study and editing interface on a separate ankiuser.net domain, so that malicious Javascript on cards can not trigger endpoints hosted on the main site. If you've found that not to be the case, or found an instance of JS not being filtered on the main site, please let us know.