When it comes to Sentence Correction problems, there are four skills that can help:
1. Patience - don't jump the gun. For the hardest SC questions, you'll need to go through a few steps before you're ready to answer.
2. Meaning - SC questions are rarely only grammatical. Be sure you understand what the original sentence is trying to convey. This will help you rule out answers that don't make sense or violate the logic or meaning of the sentence.
3. Attention to detail
4. Don't just use your gut or 'ear' to select an answer choice. Try to eliminate incorrect answer choices systematically.
There are several tools you can use to help you tackle the sentence correction problems. The Economist GMAT Tutor, for example, presents you with practice questions that incrementally get harder, testing one concept at a time and then in combination. As you progress, you will have a chance to identify these structures in more and more complex sentences.
Best of luck!