I applied to a job but my interviewer hesitated to hire me. He told me that I should work one month without salary and then he decides how to continue. What should one think about this?
Refuse. If he is not willing to pay you, you should not be willing to work. You would lose valuable time in your job research. Moreover, that's quite a shady behaviour. Do you actually want to work for that person ?
You could offer him to go through a probation period, where both parties can unilateraly terminate the contract.
Actually this is a really common situation (where I live in Italy at least) to work free for a certain period, I say that however I would never accept this kind of condition.
For me it is only a method to not pay someone for work, I am pretty sure that this will not transform into an actual working relationship (working contract).
Apart personal experience, free working is not professional unless you are in high school and you are doing a stage/internship or trainee program.
What should one think about this?
It depends on how badly you want/need this particular job, how much you trust this employer and what are the norms in your locale and domain. Consider your alternatives before making this decision.
I can't imagine doing this in my part of the world and my domain (US, software). If someone wants to hire me, they would need to pay for all of my work.
But working a free month is not typical in my space, and I'm not desperate for a job. Your mileage may vary.