With the share button, you can send a tweeted story to your Safari Reading List, copy the link from the tweet, copy the whole tweet, or send it to a friend via e-mail. The Safari Reading List feature here is my favorite because it lets me save stories from my timeline for later when I'm just in the mood to scan headlines. But it also supports sending stories to Instapaper, Pinboard, Readability, and Pocket.
Other cool stuff
Tweetbot has a number of other features that make using Twitter more efficient. You can quickly switch between your main timeline and lists you've created so you can read just the tweets you want to in the moment. You can switch Twitter accounts with only a couple of taps (once you have them set up). You can save multiple drafts if you're the type that wants to get your message just right. The app also syncs your timeline position so that if you switch to another device, you can pick up where you left off.
Tweetbot also lets you mute other Twitter users without them knowing. It's happened to everyone who uses Twitter: sometimes a specific user will go on and on with several tweets and it can get pretty annoying. Instead of unfollowing someone for just such a Twitter outburst, Tweetbot lets you mute them temporarily or as long as you want. This is a feature every twitter client should have, and it's great that it has been added in the latest version.
Tweetbot isn't perfect
For all the good things about Tweetbot, the issues I experienced are fairly minor, but worthy of note. Unlike the official Twitter client for iOS, Tweetbot doesn't show you when and how many people have followed you. There is a place to look at your followers, but I think it's important to see when and how many people follow you. After all, if you're on Twitter (or really any social network), you probably want to know when your thoughts have an impact.
The other issue won't effect everyone, but it does if you're a Twitter power user. When tweeting for a business where you need to have updates throughout the day, there is no way to schedule tweets in advance. This is a favorite feature in Hootsuite, another popular Twitter client for iOS, but sadly, Tweetbot doesn't have an option for it.
Tweetbot is an excellent client for Twitter with a good-looking layout, gesture-based controls, and almost everything you could possibly need when interacting with Twitter. It has a couple of minor issues with no summary of new followers and doesn't have the capability to schedule tweets, but these features are probably not as important to most users. But with time-saving controls, a new way to view images without leaving your timeline, and tons of other useful features, it's easy to recommend this app if you think the official client is not up to snuff.