the short answer is yes. It is hard to measure. As far as consumer health information goes its very hard to measure. The best thing you can do is look for the credentials and history of the publisher and base your confidence off of that. A while back I worked on a research team that was looking into collaborative tagging of alternative information sources as well as well respected ones to see if we could improve information retrieval accuracy. This gave us a mixed result as the crowd-sourcing nature of our data set gleamed from a social bookmarking service left us with a lot of "noise" to deal with. We ended up finding lots of simply and blatantly false consumer health information sites in our alternative sources that we had to weed out.
I think it depends on what you're measuring. Is there one item, one specific indicator or word that is measurable?
I don't know if you'd have a chance to look at 'Mappy Health'. (https://twitter.com/MappyHealth) and (http://nowtrending.hhs.gov/)
One of the co-founders is a nurse -- and this application won the HHS developers' challenge 'Now Trending: #Health in My Community" in 2012
So-- more information: http://www.govloop.com/profiles/blogs/tweeting-disease-how-mappyhealth-predicts-outbreaks
So -- MappyHealth is now running on the government sites at http://nowtrending.hhs.gov/by_tweet_places
I'm sure that they addressed the same questions you have about quality, credibility and trustworthiness...and they've been trending diseases using Tweeter for over 3 years.
Also, if you would want to reach out to Brian Norris, the co-founder of MappyHealth, he is very approachable and willing to answer questions. You can reach him on Twitter @MappyHealth
As a matter of data metrics, information quality has many dimensions--you can decide which ones are most relevant to your research questions. This is a good comprehensive list with descriptions:
To operationalize these, you probably need to go to a small panel of experts, obtain their ratings, and establish inter-rater reliability for the different types of information collected, the dimensions of quality you want to measure, and the social media platforms from which they are obtained.
I'm not sure about definitions for credibility and trustworthiness from the point of view of Information Systems studies, but you could simply create some items, pilot them, see if they work well, and create the instrument yourself. If you come up with some good antecedents of credibility and trustworthiness on social media, those would be strong research contributions.