What are the advantages/disadvantages of OpenNIC vs ISP for DNS resolution with regards to security and privacy?
You may choose a DNS server (a list is here) that logs, logs for a period, logs and anonymizes the file after a period, logs anonymously, or keeps no logs. As such, this privacy concern is well addressed in the OpenNIC project. A server owner could lie about the type of logs kept, you must judge whether you believe that is a possibility.
While I shouldn't give a statement based on my opinion, based on the resources needed to run a Tier 2 server and the type of information that could be gathered, I do not have a reason to mistrust any specific operator or the concept.
There are negligible security concerns, as the only attack a DNS server could assist is sending you to a website other than the one you requested, possibly containing malware or phishing attempts. This would be quickly addressed by the community's Tier 1 operators.
NameBench is a Google engineer's side project. It can test a large number of DNS servers to make sure that their resolution is "safe", and not a source of censorship. It will try and resolve common domain names like www.paypal.com, and make sure that they are pointing to the right location. (Not of the censorship checks are working properly at the time of this writing, but this feature still works.)
Namebench also performs speed checks. When I ran it i found out that level3's DNS resolution servers where on average 4 times as fast as the ones provided by my ISP. Also my ISP was maliciously redirecting failed DNS lookups to a spam page, which is why I was looking to replace them in the first place.