Is Kate mistaken when she disguises as a barmaid, or is Marlow the mistaken one when he becomes unreserved with Kate when he thinks she is a barmaid in She Stoops to Conquer?
The answer to this question depends on what you mean by the word "mistaken." Of course, as is shown by what happens as a result of her disguise, Kate is definitely not "mistaken" when she decides to dress up as a servant, as she not only succeeds in her goal of getting to know Marlow but also enables him to get to know her and to fall in love with her, as Marlow so ardently indicates in Act V:
But every moment that I converse with you, steals in some new grace, heightens the picture, and gives it stronger expression. What at first seemed rustic plainness, now appears refined simplicity. What seemed forward assurance, now strikes me as the result of courageous innocence, and conscious virtue.
Marlow is freed through Kate's disguise to acquaint himself with his future wife's true character in a way that would have been impossible had Kate not disguised himself, because of Marlow's timidity and reservedness when talking to women of his own station. Therefore Kate was definitely right to disguise herself.
In the same way, it is perfectly possible to argue that Marlow was not "mistaken" ultimately in being fooled by Kate's disguise, as he revealed his true self to Kate in a way that ultimately allowed them to marry, as it is only when he declares his love to Kate in front of his father and Kate's father that he is able to marry Kate. Although Marlow thus was tricked by Kate's disguise, ultimately it worked out well for him, as his freedom to express himself won him Kate's hand and brought about the happy ending demanded by this comedy.