The question regarding the strengths and weaknesses of Emily Bronte's novel Wuthering Heights is a subjective one. What this means is that different readers will find different strengths and weaknesses within the novel's text.
For some, the fact that Heathcliff's character can be defined in many different ways proves difficult for many readers. The fact that some love to hate him and other hate to love him find both sides at a continuous deadlock.
Another problem arises when readers try to place the novel in a specific genre. Some argue that the text is purely Romantic. Others argue that the text is purely Gothic. Those who do not wish to argue tend to identify it as a hybrid of both Romantic and Gothic. For some, this provides a problem given they cannot apply the specific traits of either genre to the text outright.
The themes of the novel are readily apparent. There is no question that the novel deals with love, revenge, and class conflict. The novel beautifully depicts the issues which parallel these themes and the imagery which accompanies them.
The narrative of the text can also be considered a strength of the novel. The text exists as a narrative within a narrative and supports Bronte's ingenious writing style and nature.