Updated 10/29/13:

ISU documentation on the scoring system

Program Components Overview

Program Components Explanations

Singles and Pairs documents

The link to the latest ISU communication from the ISU Single and Pair Skating documents page prompts you open a PDF, so I can't link to it directly there. Go to the link above and open ISU Communication 1790 (or whichever communication replaces it next time it's updated, probably spring 2014).

The technical panel handbooks are long documents with details on how the technical panels call elements for singles and pairs

US Figure Skating has direct links on their site to pieces of the latest ISU communication:
Singles and Pairs

Scale of Values from ISU Comm. 1790

Levels of difficulty (singles) from ISU Comm. 1790

Levels of difficulty (pairs) from ISU Comm. 1790

Establishing GOE from ISU Comm. 1790

Before addressing specific examples, especially controversial ones, make sure you have a grasp on the general principles of how the scoring system works. I (or Doris or another Golden Skate poster) could summarize in this thread, or you can read the ISU's summary.

We could probably have separate discussions of what the technical panel does, what the judges do in scoring elements, and what the judges do in scoring program components.