1. Follow every link back through the Web to its source and evaluate the original material for yourself. This is the single most important thing you can do.
Don't retweet links you haven't clicked. Don't do this from sources you know, and don't do it from sources you don't know. Just don't do it -- ever.
If you follow the chain of information back as far as it goes, as often as you can, you'll be more accurate -- and more interesting. For example, very often a link will go to an aggregation of a story that links to another original piece that contains additional information or has a different emphasis. That original report may be more important and worth sharing than the thing you'd first considered retweeting, which summarized it. But even if it isn't, at least you'll know what you're onpassing, and who and where it came from.
The whole point of blogging and a certain kind of news tweeting is to assert individual editorial judgement over the roiling Internet and re-present information in a new way. Bloggers often make news by taking someone else's 17th graf and making it their lede, providing new avenues for storytelling and reporting. That's not curation -- that's an assertion of news judgment.
Tweeting is akin to that. Reporters tweeting pieces of their own will tweet their toplines. But sometimes their "tweetable" is down deep in the piece, and not the thing they thought it was.
2. The corollary of this for visual media is to never tweet or retweet a video you haven't watched. And if you're aggregating from a video, never use the quotes someone else has in their story about what was said in the video. Watch the video yourself -- you'll often find things that things have been elided, or small words have been dropped, in the summary reports. Sometimes it's because someone has edited from raw material into story form, making a decision about what not to include for space or emphasis reasons, and sometimes it's because reporters are human, too. No matter how well-trained they are, or how prestigious the outlet where they work, humans can make mistakes, especially when they are working fast and for an editorial product with a thin editing structure. You can protect yourself from repeating other people's mistakes by confirming everything you can against available original video sources yourself.
3. Consider the source. Your best friend during a breaking-news event is a local reporter or area expert who is independently evaluating the scene or occurrence and tweeting as they go. Agencies you've never heard of but which are important to the news event are also great. If you've never heard of someone, you can Google their Twitter handle without the @ sign and you'll often get to a real identity, as people tend to use the same handles in more than one place. From there you can get a biography and begin to evaluate credibility. If someone appears to have been a troll before they began news tweeting, approach their news tweets skeptically -- they may still be trolling. Also, if someone is purportedly tweeting news about an official agency they appear to have no relationship to, compare that information to tweets coming from the agency in question. If there's no confirmation from the agency, be skeptical.