At heart, What Remains is an updated version of the country-house who-dunnit, a woman is murdered in a house that's been converted into 5 flats, and it's assumed that one of the other residents did it.
There's few tangible clues as to what happened so there's little for forensics to do - this is not CSI/Silent Witness. Instead the clues lie in the psychology and relationships of the residents - it's a bit Stephen Poliakoff in the way they're all prisoners of their pasts. So it explores the relationships of the suspects in a depth that you wouldn't normally see from Miss Marple.
Then on top of that you've got a few classic horror-movie buttons being pushed (not altogether successfully) and the hangdog detective working past his retirement date on just one last case. "You've all given up on finding the murderer, we owe it to this girl to find out what happened". It's a cliché because it works.
I can see why some people find the first half a bit slow, it's deliberately meant to be "static" and a bit claustrophobic with the vast majority of the action happening within the house. It maybe helped that I recorded it and watched the whole thing in one sitting, so didn't have a week to think about how little had apparently happened in any one episode.
On the other hand there's a few sub-plots in the middle that don't move the plot forward at all, they're just there so Giedroyc can expand his theme of loneliness in the city. It feels a bit self-indulgent when some of the residents' stories are left hanging at the end, either because he didn't know where to go or 20 minutes got left on the cutting room floor, it would be more satisfying if they had been resolved. I suppose it says something that you do care enough to want to know how things work out for them.
So this is not a show for people looking for car chases and shootouts. Personally I preferred Jane Campion's Top of the Lake which the BBC aired in the same slot a few weeks before. But if you've run out of Scandinavian detective box-sets to watch then this is a decent enough way to spend an evening.