In the same vein (ha!) Mina's attention to detail is one reason we trust her, and also, I think, believe in her as a character. She seems to have a complex mind, so much so that she threatens to go beyond the boundaries Stoker has set for her. In fact, maybe it's that threat that convinces us a character is "real"--you sense him or her straining against the prison of the medium. Still, Mina ought to have a little more room to begin with.
The other characters, especially the men, don't make it out of their cardboard boxes, in my opinion. Stoker spends a little too much time insisting on their bravery and goodness, as reported by other characters.* Their primary role is to coalesce into a collective force of good, fighting the singular but multifaceted evil that is Dracula.
Still, there is considerable complexity to their thoughts, if not to their emotions. Defeating Dracula is not just a matter of physical bravery--he must be outsmarted, and he is really smart. We get a sense of the kind of mental agility that's required in Dr. Seward's encounter with the madman Renfield, who is...well, let's just say he's a minion. So far he's mostly just been eating bugs and birds, and it's not yet clear how this is preparing him for his role in Dracula's scheme. But he is up to something:
I found Renfield sitting placidly in his room with his hands folded, smiling benignly. At the moment he seemed as sane as any one I ever saw. I sat down and talked with him on a lot of subjects, all of which he treated naturally. He then, of his own accord, spoke of going home, a subject he has never mentioned to my knowledge during his sojourn here. In fact, he spoke quite confidently of getting his discharge at once. I believe that, had I not had the chat with Harker and read the letters and the dates of his outbursts, I should have been prepared to sign for him after a brief time of observation. As it is, I am darkly suspicious. All those out-breaks were in some way linked with the proximity of the Count. What then does this absolute content mean? Can it be that his instinct is satisfied as to the vampire's ultimate triumph? Stay. He is himself zoophagous, and in his wild ravings outside the chapel door of the deserted house he always spoke of 'master'. This all seems confirmation of our idea. However, after a while I came away. My friend is just a little too sane at present to make it safe to probe him too deep with questions. He might begin to think, and then… So I came away. I mistrust these quiet moods of his, so I have given the attendant a hint to look closely after him, and to have a strait waistcoat ready in case of need.
What's interesting here is the complexity involved in trying to keep pace with Renfield's state of mind. Seward recognizes he is "too sane" to be probed "too deep"--because then he will figure out what Seward is up to. I don't know about you, but this scene reminds me of Jane Austen. You know, all the minute parsing of what so-and-so meant when he said such-and-such, and how maybe one should employ this strategy in order to elicit that reaction...These characters are not as nuanced as Austen's (although they are not that far off, the more I think about it), but all these layers of conjecture ultimately stem from a similar source: we cannot know other minds. At the same time, Seward's conjectures imply that both Renfield and he have minds--say what you will about the condition of Renfield's--and Seward struggles with the same fundamental problem real humans have: knowing for sure what others are thinking and feeling.
In other words, real humans spend a great deal of effort trying to fathom other humans' minds, and failing at it. Depicting your characters engaged in such a task, revealing both the nuances and the ultimate impossibility of the effort, is a good way of making them, or at least your story, more palpably realistic.
*This is especially the case with Jonathan. The characters keep insisting on how brave and unusually smart he is. For me, this protesting-too-much only proves that Francis Ford Coppola was right to choose Keanu Reeves for the role.