Some more data points.  Bash, /bin/sh fails while Ksh works, but emits an error:

/home/dmobrien: cat helloworld.groovy
println "hello"


/home/dmobrien: bash /usr/bin/groovy helloworld.groovy
java.lang.NoSuchMethodError: method java.util.regex.Pattern.quote with signature (Ljava.lang.String;)Ljava.lang.String; was not found.
   at org.codehaus.groovy.tools.LoaderConfiguration.loadFilteredPath(LoaderConfiguration.java:219)
   at org.codehaus.groovy.tools.LoaderConfiguration.configure(LoaderConfiguration.java:111)
   at org.codehaus.groovy.tools.GroovyStarter.rootLoader(GroovyStarter.java:88)
   at org.codehaus.groovy.tools.GroovyStarter.main(GroovyStarter.java:130)

/home/dmobrien: sh /usr/bin/groovy helloworld.groovy
java.lang.NoSuchMethodError: method java.util.regex.Pattern.quote with signature (Ljava.lang.String;)Ljava.lang.String; was not found.
   at org.codehaus.groovy.tools.LoaderConfiguration.loadFilteredPath(LoaderConfiguration.java:219)
   at org.codehaus.groovy.tools.LoaderConfiguration.configure(LoaderConfiguration.java:111)
   at org.codehaus.groovy.tools.GroovyStarter.rootLoader(GroovyStarter.java:88)
   at org.codehaus.groovy.tools.GroovyStarter.main(GroovyStarter.java:130)

/home/dmobrien: ksh /usr/bin/groovy helloworld.groovy 
/usr/bin/groovy[29]: local: not found [No such file or directory]
hello

More data:

Bash/sh evaluates to this exec line:

exec /usr/lib/jvm/java/bin/java -classpath /usr/share/java/ant.jar:/usr/share/java/ant/ant-junit.jar:/usr/share/java/ant-launcher.jar:/usr/share/java/antlr.jar:/usr/share/java/objectweb-asm/asm.jar:/usr/share/java/objectweb-asm/asm-analysis.jar:/usr/share/java/objectweb-asm/asm-tree.jar:/usr/share/java/objectweb-asm/asm-util.jar:/usr/share/java/bsf.jar:/usr/share/java/commons-cli.jar:/usr/share/java/commons-logging.jar:/usr/share/java/groovy.jar:/usr/share/java/ivy.jar:/usr/share/java/jline.jar:/usr/share/java/jsp_2_0_api.jar:/usr/share/java/junit.jar:/usr/share/java/servlet_2_4_api.jar:/usr/share/java/xstream.jar: -Dscript.name=/usr/bin/groovy -Dprogram.name=groovy -Dgroovy.starter.conf=/etc/groovy-starter.conf -Dgroovy.home= -Dtools.jar=/usr/lib/java-1.5.0/../jvm/java/lib/tools.jar org.codehaus.groovy.tools.GroovyStarter --conf /etc/groovy-starter.conf --main groovy.ui.GroovyMain helloworld.groovy


But ksh evaluates to this exec line:

exec /usr/lib/jvm/jre/bin/java -classpath /usr/share/java/ant.jar:/usr/share/java/ant/ant-junit.jar:/usr/share/java/ant-launcher.jar:/usr/share/java/antlr.jar:/usr/share/java/objectweb-asm/asm.jar:/usr/share/java/objectweb-asm/asm-analysis.jar:/usr/share/java/objectweb-asm/asm-tree.jar:/usr/share/java/objectweb-asm/asm-util.jar:/usr/share/java/bsf.jar:/usr/share/java/commons-cli.jar:/usr/share/java/commons-logging.jar:/usr/share/java/groovy.jar:/usr/share/java/ivy.jar:/usr/share/java/jline.jar:/usr/share/java/jsp_2_0_api.jar:/usr/share/java/junit.jar:/usr/share/java/servlet_2_4_api.jar:/usr/share/java/xstream.jar: -Dscript.name=/usr/bin/groovy -Dprogram.name=groovy -Dgroovy.starter.conf=/etc/groovy-starter.conf -Dgroovy.home= -Dtools.jar=/usr/lib/java-1.5.0/../jvm/java/lib/tools.jar org.codehaus.groovy.tools.GroovyStarter --conf /etc/groovy-starter.conf --main groovy.ui.GroovyMain helloworld.groovy

the difference is which java is invoked:

Bash: /usr/lib/jvm/java/bin/java
Ksh:  /usr/lib/jvm/jre/bin/java

And if I explicitly set JAVA_HOME to point to the openjdk on my machine (it was not set previously):

/home/dmobrien: whence java
/usr/bin/java
/home/dmobrien: ls -l /usr/bin/java
lrwxrwxrwx. 1 root root 22 Jun 11 03:49 /usr/bin/java -> /etc/alternatives/java
/home/dmobrien: ls -l /etc/alternatives/java
lrwxrwxrwx. 1 root root 46 Jun 11 03:49 /etc/alternatives/java -> /usr/lib/jvm/jre-1.6.0-openjdk.x86_64/bin/java
/home/dmobrien: export JAVA_HOME=/usr/lib/jvm/jre-1.6.0-openjdk.x86_64
/home/dmobrien: groovy helloworld.groovy
hello


It works.  So, the /usr/bin/groovy script is not finding the "default" java without JAVA_HOME set.

You may lower the severity since I have a work around. Thanks.

Ok, last point.  I installed the openjdk jdk and now everything works WITHOUT setting JAVA_HOME

/home/dmobrien: unset JAVA_HOME
/home/dmobrien: groovy helloworld.groovy
hello


/home/dmobrien: rpm -qa | grep java
java-1.5.0-gcj-1.5.0.0-32.fc13.x86_64
subversion-javahl-1.6.9-2.fc13.x86_64
java-1.6.0-openjdk-plugin-1.6.0.0-39.b18.fc13.x86_64
lpg-java-compat-1.1.0-4.fc12.noarch
java-1.5.0-gcj-devel-1.5.0.0-32.fc13.x86_64
javahelp2-2.0.05-8.fc12.noarch
tzdata-java-2010j-1.fc13.noarch
java-1.5.0-gcj-javadoc-1.5.0.0-32.fc13.x86_64
java-1.6.0-openjdk-1.6.0.0-39.b18.fc13.x86_64
gcc-java-4.4.4-2.fc13.x86_64
ant-javamail-1.7.1-13.fc13.x86_64
libreadline-java-0.8.0-26.fc13.x86_64
antlr3-java-3.2-5.fc13.noarch
mysql-connector-java-5.1.12-1.fc13.x86_64
eclipse-mylyn-java-3.3.2-2.fc13.noarch
java-1.6.0-openjdk-devel-1.6.0.0-39.b18.fc13.x86_64
java_cup-0.11a-4.fc13.noarch
javamail-1.4.3-2.fc13.x86_64

I guess this can be closed as "configuration issue"

Yup. Thank you for the report anyway.