Artist Disillusionment / Creator Backlash: Twitter has an API for allowing third-party clients to use the service, and this was heavily touted early on the service's life. However, as of 2014, Twitter has been taking steps to quietly encourage users to switch away from third-party clients to official ones; this is made evident by many new features such as pinned tweets and animated .gif images not functioning properly or at all in third-party clients, tweet sources no longer appearing under tweets in official clients, and perhaps most importantly, third-party clients are bound to a limit of 100,000 tokens (users); once a client hits its cap, they are no longer able to accept new users. This is possibly because Twitter relies on ad revenue, and those who use third-party clients circumvent these advertisements, which costs money for Twitter.
Ascended Fanon: Twitter likes to officially implement popular posting techniques, like hashtags, @ replies and RT retweets. Twitter is also constantly re adjusting their data handling system so that people can see photos from Tumblr and other photo showing websites.
Colbert Bump: A big part of why Twitter is so popular has to do with celebrities having taken to it so enthusiastically. And unlike most trendy things celebrities do, there's a (semi-)practical benefit to ordinary people following suit: People can now address their tweets directly to them and, supposedly, even get their attention this way.
Executive Meddling: Twitter's new API guidelines, which place stricter controls over Twitter clients, from functions to client designs.
Fan Nickname: The "Fail Whale", for the picture of a whale being escorted by birds that shows up whenever server overload prevents you from accessing Twitter.
Why Fandom Can't Have Nice Things: As much as celebrities have taken to Twitter, the very uncensored and unfiltered nature of it have also created a few enemies, due in part to some fans who air their grievances directly to the creators themselves. Some examples include people attached to Merlin, Doctor Who, and Sherlock are rather notorious examples.
Some useful Twitter utilities:
Favstar, which keeps track of a user's favorited and retweeted tweets.
Twilog, which provides an online archive of your tweets and provides some useful statistics (like tweets sent on each day and each month, times you've mentioned a user). Although Twitter itself provides a tweet archive service, Twilog's archival services are in semi-real time, while official tweet archives have to be downloaded completely every time you want an updated version. Unfortunately, the site is in Japanese only, and you can't use it if your account is set to protected mode.
Favolog, from the same developer, keeps track of the tweets you've favorited. This is particularly useful in that Twitter does not provide any official favorite archive services.
Twiprofile, a service for creating an extended Twitter bio. In addition, it provides stats about your account, such as date and time of account creation (in Japan Standard Time) and average number of tweets per day, and you can add tags to yourself so like-interested users can follow you. Japanese-only, and has the unfortunate bug of splitting lines in mid-word, as the website is not meant to be used in English.