Mi Yodeya works very well as a motley crew of advanced Shas learners, regular run-of-the-mill Torah students, and even complete beginners such as myself. What do we do, though, when a user with wonderful intentions but a middling or even lower knowledge base starts posting unsourced opinions as answers on a pretty regular basis?
Give feedback. This is why votes and comments exist.
More specifically, diagnose whatever the problem is (unsourced opinions in this case) and offer a possible solution if the answer can be fixed.
To quote someone else on a recent answer as an example:
A source would greatly improve this.
And myself on a different recent answer:
In this answer you quote Maimonides, the ancient rabbis around 70 CE, Abravanel, and the Midrash, but you don't provide references for any of them. It's hard to evaluate the correctness or quality of the answer without knowing your sources
I think that if the author edited the answer corresponding to comments like those, the answer would no longer be problematic.
This doesn't mean that the user would necessarily fix previous posts or post better answers in the future, but there is really nothing else to do. Users can be suspended by moderators, but I don't think that writing bad answers alone should be enough to warrant that.
This is not necessarily a problem (in my unsourced opinion).
Consider the following possibilities:
You don't trust me to answer a question on my own but you do trust me to apply a source from one case to another?
You don't trust me to apply a source from one case to another but you do trust me to accurately summarize what a source actually says?
You don't trust me to accurately summarize what a source actually says but you do trust me to translate a source?
You don't trust me to translate a source but you do trust me that a translation I quote is an authoritative translation?
You don't trust me to quote an authoritative translation but you do trust me to quote someone authoritative certifying a translation as authoritative?
Where does it end? At some point you either have to trust me, or better yet, have to be somewhat skeptical of everything I say. Just like you should be skeptical if I say "There is a commandment of hearing Shofar" you should be skeptical if I say "Maimonides states that there is a commandment to hear the Shofar". Again, you should be skeptical if I say "Maimonides states in Hilchot Shofar 1:1 that there is a commandment to hear the Shofar", and you should still be skeptical if I say "Maimonides states in Hilchot Shofar 1:1 that there is a commandment to hear the Shofar: מצות עשה של תורה לשמוע תרועת השופר בראש השנה". And you should be skeptical if I say "Maimonides writes: מצות עשה של תורה לשמוע תרועת השופר בראש השנה - there is a positive command of the Torah to hear the blast of the Shofar on Rosh Hashanah (my translation)".
In all of these cases you should check to the best of your ability to make sure that what I'm saying is correct. Your method of checking might be to consult someone else's translation, read the original passage, see what other users have commented or voted, etc. You should never accept something just because I claimed it.
Looked at in this light, there is not much difference between a sourced answer and an unsourced opinion. In the former you have to make sure that my answer accurately represents the source, and in the latter you have to check that my answer accurately represents Judaism. In either case, if what I wrote seems wrong you should downvote it and leave a comment explaining the problem.
Of course, answerers should as much as possible let readers know which parts of an answer need to be checked the most (e.g. by saying "this is my own application from one case to another"), but as long as an unsourced answer doesn't pretend to be an authoritative statement I don't see anything wrong with it.