请问这个句子有语法错误吗

没错

上面的都没解释你知道 the only person known about this 的意思其实是唯一的在这方面出名的人
known about this 是动词的过去分词做宾语补足语 =who was known about this.

有错。
首先you后是were
其次从句中的先行词前有the only 限定，其后必须有关系代词。
而且即使没有the only 限定，person也是kown的逻辑主语，是应该加关系代词的。只有当这里的person是它后面动词的逻辑宾语时才可以省略关系代词的。

I was glad（that) you were the only person that knew about this.

没有错误

这类句子你看一个例句；

He is a kind person called LeiFeng。

i was glad（that) you was the only person known about this.
known 做过去分词用,如果要用who来引导的话，就要这样说：
i was glad （that) you was the only person who knew about it.

明白了么？

呃……错了哦。帮你改改吧。

I was glad (that) you were the only person who knew about this.

was改为were，known改为knowing
很明显嘛！