The 3.1 distribution will run on OS X.
Tested with OS X 10.4, Java 1.5.0_16, Tomcat 5.5.27
The truststore location seems to be defined for a Windows machine in conf/omar.properties.
If it is not defined correctly, the result will be a number of security errors.
Locate the truststore properties in omar.properties and change it to reflect the location of the cacerts file.
# The keystore storing the certificate of trust anchors
#
#omar.security.trustAnchors.keystoreFile=/j2sdk1.4.1/jre/lib/security/cacerts
omar.security.trustAnchors.keystoreFile=/System/Library/Frameworks/JavaVM.framework/Versions/1.5.0/Home/lib/security/cacerts