If the guest is complaining about the hotel system and by the system he is wrong should the Guest relation officer put it to the Daily Report?

Yes, of course. If a customer is troubled or thinks any system is wrong means there are some others who also think this way. The customer should be assured that the authority will work on that. The Guest relation officer should report that giving priority so that it could be satisfactory as early as possible.

No, as this is a routine experience when the customer complains without any deficiency in the system.

if this is added to the daily report, the report looks awful.

Yes, of course , the " Guest relationship officer", should put on " Daily Report".