You should think it clearly whether he is eligible for the job. 有无语法错误

我觉得应该在whether前加上that更好。
You should think it clearly （that）whether he is eligible for the job.

因为你要考虑清楚的事情是他是否胜任工作，think后面it作宾语，但是it指代的是whether he is eligible for the job.，所以应该在这句话前加上that，用以引导这个句子。

非常正确啊。

去掉it.
You should think clearly whether he is eligible for the job.

think在此处不能作及物动词，改为think it over较好，意思为仔细考虑，这样clearly就不需要了。
You should think it over whether he is eligible for the job. 没别的问题啦！