FYI, the Seamonkey 2.12 release notes (the version that just came out, updated in Slackware 13.37 and -current) says under Known Issues:
The Java 7 plugin does not work with SeaMonkey (bug 754622).
I have not found this to be true. I have the Sun Java 7u7 plugin on Seamonkey and it seems OK. I think maybe the bug report was specific to Debian/Ubuntu or something about having multiple JRE versions installed.