A Japanese equivalent to "a seal" in the context is "(裁判所の)認証印."

”By law" is "法定の" or "法で定められた."

"A court of record" is sometimes translated as 記録裁判所. This Japanese
may not always convey the meaning of the original English. I would put it in Japanese as "(判決について) 拘束力のある裁判所" if I summarize the following article about a court of record.
http://en.wikipedia.org/wiki/Court_of_record

"Superior Court which is a court of record having by law a seal" will be "法定の認証印を有する記録裁判所である上級裁判所(または高等裁判所)” or "法定の認証印を有し拘束力を持つ上級裁判所(高等裁判所)."