(Disclaimer, I am in no way a writing expert, a TV expert,a series expert or an anything expert so please please please don't take anything I say as solid word on this; this is purely my own thoughts and opinions on it all.)
So let's begin. (There may be spoilers so please only read if you've seen all three series)
Firstly, it passes the Bechdel test, which if you didn't know, means that the series has at least two named female characters who talk to each other (have solid back and forth dialogue), about something other than a man. It's usually applied to films and believe me you'd be amazed at how many fail the test...Harry Potter and The Deathly Hallows Pt 2? The entire Lord of the Rings trilogy? The oh so beloved Original Star Wars trilogy? You see where I'm going with this.
This leads nicely onto my second point. Across the whole of the three series all of the characters we meet, although some are shrouded in mystery, are well rounded and fully developed and they are all flawed human beings. Each character serves a purpose. They're all believable as real people in a small seaside village. You develop some kind of connection with every character, you're either rooting for them or hate them or laugh at them or feel sympathy, and you don't get that with two dimensional characters. It's what makes the series so interesting, because as well as being invested in the plot, you're invested in the lives of completely fictional characters.
Along with that, the relationship dynamics between the characters are so well written. You've got the contrast between Alec Hardy and Ellie Miller, the moody DI and the chirpy DS at base level, the characters work together brilliantly because their dynamic creates a low level of conflict, they both have the same end goal but different reactions to case developments and different ways of tackling things, just like real people do. They develop an odd sort of friendship which feels very genuine. You really see their working relationship grow and the dynamic changes as the case goes on (in the first series) and continuously develops through the second and third series.
Then you have the Latimers', a family dynamic which is strained after the murder of their son in series one. We get to see the effect this has on a marriage, a mother daughter/father daughter relationship and it all feels very real. They band together, they become volatile, there are explosions of emotion littered throughout each series. The beauty of Broadchurch is that it doesn't just drop the relationships into black and white territory, it's incredibly rare that the characters have straight up opposing view points, they all have their own complex reasoning and motives behind everything they do.
In the third series we see how the Latimers' are coming to terms, in different ways, with Danny's death and the fact that Joe Miller was found not guilty despite his initial confession. We see the effect this has had on their relationship, Beth and Chlo are trying to move on with their lives, while Mark is stuck focusing on the loss of Danny and is trapped in his own guilt and grief as a father. We watch the turmoil they all go through, each in their own unique way, and how this essentially tears the family apart. Beth and Mark still care for each other deeply but it's clear the emotional damage of losing a child and the way they each deal with that has had an impact on their relationship.
Broadchurch doesn't shy away from not giving the viewers what the want.
In an ideal world the heartbreak would have of course brought them closer together, and in some ways, it has, but ultimately it spells the end of a marriage and the breakdown of a father to the point of attempting suicide.
I could write for days about the complexity of the plots in each series, but I think all I need to say is, that guessing who killed Danny, will Joe get off, and who raped Trish, has been the main topic of conversation in many a work place and in many a coffee shop. There are enough twists and turns to keep you interested but not so many that you can't follow what is happening. The array of characters has you constantly speculating. Just like all good TV drama should.
The show is unlike most detective 'who dunnit' shows on TV for one main reason. It focuses on the people, the raw human reaction to the crime that has taken place. It focuses on the emotion that atrocities such as murder and rape draw out of people. It picks apart the volatile nature of the court of public opinion. It tackles irresponsible journalism and the dark turn it can take. Ultimately it highlights, interrogates and forgives the fundamental flaws of human nature.
AND THAT IS WHY WE NEED MORE WRITING LIKE BROADCHURCH.