1. A Tweet written and submitted under the influence..
2. using twitter with enough drinks, narcotics, stimulants, pain killers, mood enhancers..etc..to alter the normal 'Tweets'.
3. Like a DUI, with a keyboard, not a car....
4. Tweeting something you would not normally tweet...but liquid or other courage lowers inhibitions, and results in 'tweets' with either too much information, or something embarrassing.
5. Writing a 'tweet' that would normally be omitted, or without controversy, but due to alcohol, etc. the tweet is written, and likely deleted the next morning.
Note: TweetUI is exponentially likely worse as your number of followers increases, or is in the thousands or more.
Dude thought tweeting Jeff Foxworthy quotes would get him a chick. 7 Beers and 3 tweetUI's later, he realized he was living in the early 2000's.
Sandy, normally shy, hit the bar, did the producer, and wrote a tweetUI about the experience. She awoke and deleted the ill-fated tweetUI.