We literally just finished the series an hour ago. Here's my advice for potential new watchers - if you lean more towards the tone of David Fincher crime films then you'll enjoy the back-half of the series more, however, if you lean more towards the tone of Paul Feig films then you'll enjoy the first half of the series more. If in doubt, watch the film first.
I believe the second audience types are responsible for most the narrative surrounding the latter seasons and I understand their frustrations (this is almost a completely different series by the end of it). However, I personally disagree with what seems to be the general consensus here regarding when the series was at its best.
My experience: I saw the film in theatres when it first came out (first introduction to Luther) and my family and I really enjoyed it. We started the series and...absolutely hated it; terrible writing, ridiculous plotting, unbelievable leaps in logic by Luther, etc all of this from the get-go. I wanted to stop watching pretty quickly, however, I was out-voted ("in case it gets better").
Fast forward five seasons, whole family agrees that it actually got much better the further it went - against the usual narrative I see in these threads. IMO, the series' writing improved drastically as the seasons went along and ultimately shed its more absurd elements and soap-opera trappings. Season 5 was the best season for us and we're greatly looking forward to rewatching the film.