英语,有语病否?many students graduate unaware of the best methods of searching for a job.

正确,没有语法错误.
1 unaware of the best methods of searching for a job可以说是many students的后置定语,现在放到谓语动词的后面了,目的是避免头重脚轻.
2 unaware of the best methods of searching for a job也可以说是主语补足语,用英语句子表达就是：Many students are unaware of the best methods of searching for a job when they graduate.
3 再补充一句有主语补足语的句子：
He often goes to bed hungry ==He is often hungry when he goes to bed.