- Ellie is currently not in a good state of mind. Killing the slug is a way to showcase that. Ellie is not feeling well, as her character is usually much softer and well-spirited.
- It also hints at how she is going to approach life now that Joe is revealed to be a murderer. Killing the slug insinuates that it is a lower form of life compared to Ellie, and that it must be taken away because Ellie wants it to be. The symbolic suggestion is that Ellie will think the same way of Joe: He's a lesser human being, not worthy to be in her life.
- One review I found argues the symbolism of the snail. It is first revealed in episode 2, to suggest that "something is wrong in Ellie's house". After Joe is revealed, the snail is killed (thus symbolizing Joe (the bad presence)'s removal from Ellie's life).
From the review:
After all, this is a case of expecting the wife of an abuser to know exactly what is happening, rather than seeing that the blame truly lies with the man who committed the crime, regardless of the women surrounding it.
Somewhat strangely, this particular point is represented by a slug. This is seen in episode two, never mentioned or explained but intended to represent, according to creator Chris Chiball, “that things are wrong in [Ellie’s] house”. In the final episode, after the murderer is revealed, the slug is trodden on.
Broadchurch stresses the pressure on mothers to ‘know’ and encourages the audience to understand that abuse is the abuser’s fault and no-one else’s. ‘Slug-gate’ is so subtle that is arguably only effective in hindsight and I think that is what makes Broadchurch so clever and absorbing. It’s not trying to deliver any moral maxim, but its social observations are there, lurking beneath the surface of the narrative, intended to make you think.