Hi emlawson12,
By default, the paperclip icon in the list only display whether the item has attachments.
In SharePoint 2010, we can customize SXL for the list web part using SharePoint Designer to displaying attachments.
1. Open list view in SharePoint Designer, and insert column to right/left as you want.
2. Find the da tag of the new inserted column.

2. Chang it to the following XSL:
<td id="ItemAttchment">
<xsl:element name="SharePoint:AttachmentsField">
<xsl:attribute name="runat">server</xsl:attribute>
<xsl:attribute name="FieldName">Attachments</xsl:attribute>
<xsl:attribute name="ControlMode">Display</xsl:attribute>
<xsl:attribute name="Visible">true</xsl:attribute>
<xsl:attribute name="ItemId">
<xsl:value-of select="@ID"/>
</xsl:attribute>
</xsl:element>
</td>

3. Save the view. Then back to the list in browser, refresh the page and check the results.

Read the following blog for more detail steps:
http://amitphule.blogspot.sg/2012/04/display-item-attachments-in-sharepoint.html
Best Regards,
Linda Zhang
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