There have been various attempts to understand trends from this data, with MIT for instance producing research into what kind of tweets traditionally get shared and retweeted most frequently. Researchers from Microsoft have added their own thoughts to the field, with a paper looking at whether the interest level of a tweet can be predicted.
To test this, the researchers took a crowdsourced approach whereby individuals were sourced to personally rate and label particular tweets as interesting or not. This process was preceded by a survey sent to participants to actually ask them what made a tweet interesting for them.
The responses to this question were then grouped according to whether they related to the context the tweet was made in (ie for news stories), or the content itself (ie whether it was funny).
From this survey, it emerged that the source of the tweet was the most important, with those from reputable sources increasingly regarded as interesting, with social proof metrics such as the number of retweets proving spectacularly unimportant to users.
The labeling process was much less conclusive however, with the participants proving about as successful as identifying any interesting tweets as you would expect from a random sample.
So, unfortunately, if you're on the hunt for the holy grail of what will make a tweet interesting, it's fair to say that this paper will leave you to continue your search elsewhere. Given the complex nature of Twitter however, the researchers were at pains to point out the subjectivity of what people found to be interesting, and there in lies the challenge for all of us. With each individual baring unique traits and characteristics, the ability to narrow those tastes down via an algorithm will have to be something for the next team of researchers.