Am I the only one not comfortable using DNS servers running by random volunteers? Is there any "vouching" of the operators or regular checks on common domain on those OpenNIC servers?

Well, my computer runs a bunch of software written by random volunteers so personally I'm not that worried about it. I personally prefer that to the available alternatives. Yes it would be great to have monitoring (of all the dns services) and I'm not sure if anyone does that, but considering the perpetual tran wreck that is DNSSEC it doesn't really alter anything as all dns is vulnerable.

With https, whoever you end up contacting needs to cough up a valid certificate for the domain in the url. I run https everywhere to try to get that protection as often as possible. In practice there are still ways that dns tricks can cause trouble but they are not as bad as you might think and browsers are slowly pushing an https only web (I hear Chrome will soon start marking all http sites as "insecure" rather than https sites as secure). ssh has its own authentication method and I do try to verify new hosts via another secure chanel.

Speaking of not trusting companies, I am reminded that at one point I noticed that CentryLink seems to be intercepting all dns traffic no matter the intended destination, so without either a secure connection past the ISP or maybe a nonstandard port it may not matter what dns server you try to use. Hopefully all ISPs that do this do the horrible redirect of invalid domains thing so attempting an http connection to an invalid domain might show if this is the case (I found it trying some of the nonstandard domains that OpenNIC resolves).

You're definitely not alone. This sounds a little too Tor-ish for my taste.