I'd say Stoker struggles with this in the case of Van Helsing. One problem is that the readers know what's happening to Lucy--i.e. she's having the mortal life drained out of her night after night by the Count--but the other characters don't. This makes for a certain type of suspense, but also necessitates some rather unbelievable choices. For instance, Jonathan, recovering in Budapest from his ordeal in the Castle Dracula, hands his quite informative diary over to Mina, but tells her he never wants to read it again, and she agrees never to read it except in the most dire circumstances. He wants to put the horrors all behind him, see. Meanwhile the nuns taking care of him know darn well what's happened, but they won't speak of it because it's unholy.
And Van Helsing, while implementing various temporarily effective treatments against vampire visits, tells no one of his suspicions--ostensibly because he wants to be sure, before he makes such an extraordinary claim. But this leads him to not sufficiently explain the importance of various measures--namely Don't Open the Windows and Don't Take off the Garlic Necklace for God's Sake--to the other characters, including Lucy herself. Also, conveniently, Lucy's mother has a fatal heart condition, which means she can't be told anything, lest she risk dying of shock. Which, spoiler, she does anyway. And Lucy's fiance's father is sick also, so he has to be away and can't help out much. Etc.
Van Helsing also has a way of being in Antwerp, or asleep in a chair, when he is most needed. But is he just being pushed out of the way by Stoker in these cases to make way for the plot? Or is there something about Van Helsing himself that makes him a flawed expert--and perhaps a more realistic character in the bargain? We are given to understand that Van Helsing has a sly sense of humor and a big personality. Also he's foreign, so he talks funny.
How appealing these features actually are, is another question:
Found Van Helsing in excellent spirits, and Lucy much better. Shortly after I had arrived, a big parcel from abroad came for the Professor. He opened it with much impressment, assumed, of course, and showed a great bundle of white flowers.
"These are for you, Miss Lucy," he said.
"For me? Oh, Dr. Van Helsing!"
"Yes, my dear, but not for you to play with. These are medicines." Here Lucy made a wry face. "Nay, but they are not to take in a decoction or in nauseous form, so you need not snub that so charming nose, or I shall point out to my friend Arthur what woes he may have to endure in seeing so much beauty that he so loves so much distort. Aha, my pretty miss, that bring the so nice nose all straight again. This is medicinal, but you do not know how. I put him in your window, I make pretty wreath, and hang him round your neck, so you sleep well. Oh, yes! They, like the lotus flower, make your trouble forgotten. It smell so like the waters of Lethe, and of that fountain of youth that the Conquistadores sought for in the Floridas, and find him all too late."
"Not for you to play with?" "You need not snub that so charming nose?" Oh, ICK. I know all the other characters treat Lucy like a child, and that is meant to indicate both their kindness and her irresistible womanly innocence. But Van Helsing's supposedly erudite babbling, combined with this condescension and the weird attempt at having an accent, just does not inspire confidence.
The scene above goes on:
Whilst he was speaking, Lucy had been examining the flowers and smelling them. Now she threw them down saying, with half laughter, and half disgust,
"Oh, Professor, I believe you are only putting up a joke on me. Why, these flowers are only common garlic."
To my surprise, Van Helsing rose up and said with all his sternness, his iron jaw set and his bushy eyebrows meeting,
"No trifling with me! I never jest! There is grim purpose in what I do, and I warn you that you do not thwart me. Take care, for the sake of others if not for your own." Then seeing poor Lucy scared, as she might well be, he went on more gently, "Oh, little miss, my dear, do not fear me. I only do for your good, but there is much virtue to you in those so common flowers. See, I place them myself in your room. I make myself the wreath that you are to wear. But hush! No telling to others that make so inquisitive questions. We must obey, and silence is a part of obedience, and obedience is to bring you strong and well into loving arms that wait for you. Now sit still a while..."
I think we are to take this sudden flare-up of temper, add it to the general loopiness of speech and affect, and be convinced that Van Helsing is eccentric, and therefore a genius. His frequent lapses in the early going are meant to be products of circumstance, not results of his own failings.
But what if the reverse were true? What if he is a self-defeating genius, one who secretly has a fear of success and so undermines his own efforts with trips to Antwerp? What if, deep down, he admires the Count and wants to be a vampire himself--so that his tormented subconscious causes him to carry out the Count's wishes even as he seems to be fighting him?
As I say, I'm pretty sure this is not what Stoker is up to. He's just not that much for characterization, even though I think there's more to his characters than other books of this ilk tend to offer. But for those of us who want to bring experts into our own fiction--without wrecking either the story or the belief in the character's competence--the self-defeating expert could be an option.