Learn English – word to (best) describe someone who sees and remembers every single thing

I think it depends on the person and his/her perspective on the matter.

For instance, someone who recognizes that humans are flawed but believes in their fundamental goodness nonetheless could be described as forgiving, good-natured, tolerant or benevolent.

Someone who has faith in others to do the right thing (and potentially doesn't see or overlooks their character flaws) could be described as trusting or idealistic.

If we, knowing as we do that people are rather nasty creatures, describe such a person from our cynical vantage point, we might call him/her credulous, naive or unsuspecting.

The verb 'to visit' carries this connotation and is the term used referring to sick people: (from TFD and dictionary.reference.com)

To visit:

• to go to see in order to aid or console: visit the sick and dying.
• to come to in order to comfort or aid: to visit the sick.