I have pretty simple schema:

CREATE TABLE Customer (
customer_id INTEGER NOT NULL,
name VARCHAR(100) NOT NULL,
...
);

CREATE TABLE Attribute (
attribute_id INTEGER NOT NULL,
name VARCHAR(50) NOT NULL,
description VARCHAR(255) NOT NULL,
...
);

CREATE TABLE Customer_Attribute (
customer_id INTEGER NOT NULL,
value FLOAT NULL,
score FLOAT NULL,
attribute_id INTEGER NOT NULL
);

Hibernate mapping looks like this:

<class name="com.pa.pharma.customer.Customer" table="CUSTOMER" dynamic-update="true" >
<id column="CUSTOMER_ID" name="id" type="long">
<generator class="native"/>
</id>

<property column="NAME" length="100" name="name" not-null="true" type="string"/>
<map name="attributes" table="customer_attribute" lazy="true" >
<key column="customer_id" />
<index column="attribute_id" type="long" />
<composite-element class="com.pa.pharma.segmentation.CustomerAttribute" >
<property name="score" column="SCORE" type="double" />
<property name="value" column="VALUE" type="double" />
<many-to-one name="attribute" class="com.pa.pharma.segmentation.Attribute"
column="attribute_id" outer-join="true" update="false" insert="false" />
</composite-element>
</map>
</class>

After installing Hibernate 2.0.3 I've got an exception:
net.sf.hibernate.MappingException: Repeated column in mapping for
collection: com.pa.pharma.customer.Customer.attributes column:
attribute_id

Previous versions 2.0.1 and 2.0.2 works fine.

This is weird to have the index of a collection (attribute_id) which is also the FK to a many to one.

Actually my intention was to create mapping similar to this http://www.hibernate.org/118.html#A10, but instead of set use map in order to have an ability to lookup attribute value by attribute id. What was wrong in my approach?

Have a look at the doco and the behavior of the index attribute. It's related to index of collection, not pk or fk at all.