Comparison of ELU.SE and Wiktionary policies
Votes and opinions on StackExchange are definitely not the basis for any edit to Wiktionary, just like the mere existence of a definition on Wiktionary does not make said definition a good answer on StackExchange. So, in principle, no circularity is possible.
However, Wiktionary and StackExchange have matching goals: respectively they aim to be based on references (plus NPOV) and objective. They might differ in how lax their criteria for inclusion and attestation, but if there is a severe mismatch in definitions and so on then something probably went wrong on either site. So, in case of conflict between Wiktionary and SE entries, it's fine to use the best curated of the two to improve the other. (Here I linked the English Wiktionary policies, but the principles are the same on all Wiktionary subdomains.)
StackExchange process for mistakes found via Wiktionary
If you find a mistaken StackExchange post, you can add a correct answer, mentioning your sources, and hope to eventually get enough popularity and upvotes to reach the top. Do kindly comment the other answers to point out why you think they are wrong, and so on.
Wiktionary process for mistakes found via StackExchange
If you find a mistaken or otherwise improvable Wiktionary entry, do edit it yourself, or encourage to edit it, in compliance with the Wiktionary policies above.
- Make sure to reference your sources and explain your rational arguments.
- If the matter is particularly complex or controversial, remember to use the history page and talk page to find out why the entry was that way and to explain your reasons. The more solid your references, the bigger the changes you can make. Wiktionary consensus is based on rationality and discussion, not votes.
- Do link the StackExchange post for context and transparency, especially if there is more content into it than the source you mentioned; but add such links in the edit summary or talk page, because StackEchange is not a valid source in itself.
Legal obligations when using Wiktionary on StackExchange or vice versa
If you quote or reference Wiktionary material, make sure to link the Wiktionary entry, both for attribution and so that the user can reach the most recent and better version (the entry might even be improved by you or other StackEchange users, per above!). I'd even argue that a link is more informative than a quotation, given Wiktionary revisions are going to stay there forever and no information loss is possible, while quotations can quickly get outdated. An exception is when the Wiktionary entry is very big or in rapid flux, making it hard to understand what part of it you are referring to (think of the entries with dozens of meanings).