Experience with the subject matter in question, and ability to back up the opinion with reasonable argument and facts. E.g.:
-"Free trade is good/bad!" I'd be very wary of giving out such an opinion, since I have very little knowledge of economics, so I couldn't really call my opinion valid.
-"Climate change is a threat to the future of human civilization." I'm a bit more confident giving out that opinion, since I studied environmental management in uni (since changed gears career-wise), and I feel I can back that opinion up within historical context (shifts in climate in Earth's past and its effects on humans and other species), contemporary context (rising sea levels, lack of polar ice, spread of disease (e.g. malaria), heatwaves, temperature records, etc.), and societal context (question of 'climate refugees,' which is a hot topic in the Pacific for instance). I'd be wary of engaging in debate with an actual climate scientist for instance, but on the everyday level, I'd feel a bit more at ease.
Or, to top it off, "work of fiction a is bad/good." That's a perfectly valid opinion, as long as you've actually seen/read/played it firsthand. It's why I try to avoid directly mentioning Twilight/50 Shades of Grey, as I've never read/seen them bar some of the first Twilight novel, so despite widespread opinion, I don't feel at ease outright stating them to be bad. I'm probably not always innocent of not falling into such mindsets (e.g. aware of Uwe Bowl, even if I've never seen any of his films), but, well, I try.
Then again, there's always the idea of opinion flying in the face of consensus. For instance, I think 2001: A Space Odyssey is a lacklustre film. I'm not so deluded however, as to not recognise that I'm in the minority of thought in that area, and that I can't deny its influence on the genre.