When applying for a job, it's important to have  the skills and experience needed for the job.

这个句子没有任何问题。

When 从句的这种省略主语，是泛指“任何人”。在主句中即便没有“人”的主语，也正确。如果补全的话，就是：

When we/you are applying for a job, it's important to have the skills and experience needed for the job.

这里，we 和 you 泛指“任何人”。