I'll add something since I need to take a break from brief research...
LEEWS focus on teaching you how to analyze and write an exam. The key point here is to argue both sides, and then choose the one you think is strongest. My contracts prof last semester talked about it in terms of "forking" your answer.
Taking your negligence example, you know the rule (Injury, Duty, Breach, Cause).
So you read your hypo, and see that A has a possible negligence claim against B. So you discuss. You take the duty element, and say what A's argument is that B had a duty towards A. Then you rebut w/ B's defense/counter argument. You decide which is better. If you think A's arg is better, then you say so, and move on to Breach. However, even if you say B's argument is better, you still may want to move on and discuss Breach, saying something like "despite B's stronger argument, the court may find for A in the matter of duty, and would then discuss breach."
The tricky thing is to try to focus on the main issues, and address the "smaller" issues as a secondary concern. Many people get bogged down in the smaller points and loss valuable analysis time on the meaty issues the prof's really after. An example of this would be a negliegence discussion where duty and breach are extremely straightforward, but cause is the big ticket item. My torts exam was heavy on the duty questions, with some big causation issues thrown in. You don't want to write 5 paragraphs on an easy duty issue when the prof values your causation analysis more.
Arguing both sides and choosing the strongest point is how you apply the black letter law. This is what LEEWS teaches you. While the issue spotting exam may not apply everywhere, the skill of practicing arguing both sides will likely help in most law school exams you take. LEEWS also has some good advice in terms of how to approach a 3 page hypo with a final instruction of "discuss all claims" without getting overwhelmed.
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