GeoServer requires special configuration to run in WebLogic out of the box:

• In the Weblogic console, set "Enforce Strict URL pattern" to false
• If you're running GeoServer older than 1.5.1 and want the make map previews work:
  1. unpack geoserver.war and deploy as a folder
  2. make sure the "preview" directory inside the GeoServer is writable
  3. add the followin section to GeoServer web.xml file:

     <mime-mapping>
        <extension>xml</extension>
        <mime-type>text/xml</mime-type>
     </mime-mapping>

• starting with version 1.6.1 GeoServer added a transparent gzip compression filter
  to speed up page/gml/gml serving, and that does not play well with WebLogic, which
  will re-compress it and thus break the browsers trying to interpret the contents.
  The solution is to disable the GeoServer compression filter by removing or commenting it
  out (both the filter and its mapping):

  <!-- 
    <filter>
       <filter-name>GZIP Compression Filter</filter-name>
       <filter-class>org.geoserver.filters.GZIPFilter</filter-class>
       <init-param>
           <param-name>compressed-types</param-name>
           <param-value>text/.*,.*xml.*,application/json,application/x-javascript</param-value>
       </init-param>
     </filter>
  -->
  
  ...
  
  <!-- 
    <filter-mapping>
      <filter-name>GZIP Compression Filter</filter-name>
      <url-pattern>/*</url-pattern>
    </filter-mapping>
   -->

We'd like to thank Luca Morandini and Jason Taixing for providing these informations.