It's strange he has a moustache, because when he's Dracula as an old man in the scenes in the castle with Harker in the beginning he doesn't have one... Perhaps it grew when he was on the ship to London.
But also he can shapeshift into different forms, so growing a moustache suddenly should perhaps not be a problem either.
There also is a mini-series with Patrick Bergin as Dracula where he has a moustache. It's not rated highly and I suppose not great, but I kind of liked it:
Dracula (TV Series 2002– ) - IMDb
It has an Italian vibe to it, it was done for Italian television.
Maybe they leave out the moustache in a lot of adaptations, because it accentuates the fangs more?
Dracula is actually the literary equivalent of a found footage film. You could film it as such if you set it in modern times. Harker taking a camera to the castle: 'So, this is my first night at the castle.' And Seward filming Renfield for study at the asylum, Van Helsing having his methods filmed etc.
It might work if found footage was done in a more adult way, often it's rather juvenile with characters constantly joking, which lets it down often.