Still, if it sounds a bit leaden, it is nothing compared to some of the script lines, which sound as if the show's script writers have been slipped a few quid by some Eurocrat from the Commission for the Defence of the European Arrest Warrant.
Whenever our Euro-heroes are frustrated in their work, for example, they mutter things along the lines of: "If only we had a pan-European arrest warrant, that serial killer would be behind bars by now." To which their partner will nod solemnly and reply: "Yes, if only sovereign law enforcement agencies cooperated more closely in jurisdictional issues..." I am paraphrasing somewhat.
Because in order get around these gripping bureaucratic and jurisdictional issues – and to actually nab a few villains – the team are issued with arrest warrants provided by a contact at the International Criminal Court in The Hague, played by Donald Sutherland.
This allows them to investigate serial killers and drug traffickers over the parochial objections of local police forces like Scotland Yard – despite the fact the ICC normally only investigates things like genocide and war crimes.
As Kevin Jon Heller, an expert in international criminal law who also happens to be a Hollywood TV script writer, wrote in this analysis here: "You don’t have to be an ICC expert to realise that the show’s treatment of the Court’s jurisdiction is a fiasco." So how, then, did it get made?
One possibility, perhaps, is that it had secret funding from the EU, which, after all, already bankrolls things like Euro News, Brussels' own answer to CNN.
The Government has been battling with Eurosceptic Tory MPs over the controversial European Arrest Warrant, which it claims is not such a bad thing after all.
The Home Secretary, Theresa May, has been blizzarding rebel MPs with arguments in its favour, claiming that Britain will become a "safe haven" for all kinds of Euro-criminals if it backs out of it, and that procedures have been tightened so that British holidaymakers will no longer languish for years in a Polish jail after failing to tip a waiter, or whatever.
I've no doubt that the formidable Ms May needs no help in convincing her opponents.
But if she's struggling, she might try showing them an episode of "Crossing Lines" – a detective series broadcast on the American channel NBC, and arguably the world's first ever "Eurocop" show. No, I hadn't heard of it either, and had I not been idly channel-surfing one night, this "action-packed global crime drama" would have passed me by entirely.
But if you've ever wondered what a cop show would look like if it were written by an arch Euro-federalist like Jean Claude Juncker, read on. A team of cops from all around Europe – think Wallander, Hercule Poirot, Van der Vaalk and Sarah Lund all rolled into one – charge around the continent in pursuit of various villains. And in Crossing Lines, that twist is the ever-present threat to justice and good order posed by the lack of a European federal superstate.