Sam insisted that he hadn't broken the law and not be punished.

这个句子，在insisted之后跟了两个并列的that从句：

第一个that从句是：that he hadn't broken the law

第二个that从句，缺少that和主语，应改为：that he not be punished.

Sam insisted that he hadn't broken the law and that he (should) not be punished.

insist 有两种用法：当它坚持认定一个发生的“事实”时，其宾语从句不用虚拟语气；当它坚持一个“主张”时，用虚拟语气（should + 动词原形，should可省略）。例如：

The thief insisted that he had not stolen anything from the supermarket, but the manager insisted that he (should) be sent to the police station. 小偷坚持说他没有从超市偷任何东西，但超市经理却坚决主张把他送到警察局。

suggest 也有类似用法：当 suggest 表示“建议”时，宾语从句使用虚拟语气。当它表达“显示，暗示”意思时，则不用虚拟语气。例如：

The smile on his face seemed to suggest that he was happy to have lost his life for his country. 他脸上的笑容似乎暗示出他很高兴为自己的祖国献出了生命。

Statistics suggest that more and more full time students are taking up part time work. 统计资料显示，越来越多的全日制学生正在从事一些兼职工作。

suggest 宾语从句使用虚拟语气的从句（略）