Is there a situation where the ID is available for use in a criteria but other properties are not?

This works:
session.CreateCriteria(typeof(Move)).Add(Expression.Eq("Actor.Id", 1)).List();

This does not:
session.CreateCriteria(typeof(Move)).Add(Expression.Eq("Actor.Name", "Alphonse")).List();

Here is a snippet from Actor.hbm.xml (I removed properties for brevity):
<?xml version="1.0" encoding="utf-8" ?>
<hibernate-mapping xmlns="urn:nhibernate-mapping-2.0">
<class name="SR.Tactics.Actor, TacticsDAL" table="actors">
<id name="Id" column="id" type="Int32" unsaved-value="0">
<generator class="native"/>
</id>
<property column="name" type="String" name="Name" not-null="true" length="20" />
</class>
</hibernate-mapping>

for you to add expression to another entity properties using Criteria you need to use CreateAlias or CreateCriteria API

I'm not sure what you mean. What is CreateCriteria API?

you can using something like this

ICriteria c = s.OpenSession().CreateCriteria(typeof(Product));
c.CreateAlias("Type","t");
c.CreateAlias("t.Color","c");
c.CreateAlias("c.Location","l");
c.Add(NHibernate.Expression.Expression.Eq("t.Name","Computer"));

Thanks ryzam. That worked well.