Is there a custom FxCop rule that will detect unused PUBLIC methods?

Corey, my answer of using FxCop had assumed you were interested in removing unused private members, however to solve the problem with other cases you can try using NDepend. Here is some CQL to detect unused public members (adapted from an article listed below):

// <Name>Potentially unused methods</Name>
WARN IF Count > 0 IN SELECT METHODS WHERE
 MethodCa == 0 AND            // Ca=0 -> No Afferent Coupling -> The method 
                              // is not used in the context of this
                              // application.

 IsPublic AND                 // Check for unused public methods

 !IsEntryPoint AND            // Main() method is not used by-design.

 !IsExplicitInterfaceImpl AND // The IL code never explicitely calls 
                              // explicit interface methods implementation.

 !IsClassConstructor AND      // The IL code never explicitely calls class
                              // constructors.

 !IsFinalizer                 // The IL code never explicitely calls
                              // finalizers.

Source: Patrick Smacchia's "Code metrics on Coupling, Dead Code, Design flaws and Re-engineering. The article also goes over detecting dead fields and types.

(EDIT: made answer more understandable)

EDIT 11th June 2012: Explain new NDepend facilities concerning unused code. Disclaimer: I am one of the developer of this tool.

Since NDepend v4 released in May 2012, the tool proposes to write Code Rule over LINQ Query (CQLin