There's a lot of criticism by the local people against Helsinki being too car-friendly. Pedestrian crossings deemed dangerous being simply removed rather than putting traffic lights to tame the cars instead. Large multi-lane roads right outside the densest city centre. Too much space allocated for cars vs pedestrians and other light traffic in the city centre area where the latter outnumber the former by 10x.
The only thing that directly supports the zero-death record is the lower speed limits. They used to be 50 km/h some decades ago, then most of the city centre was lowered to 40 km/h and now in the last 10-15 years there's been a proliferation of 30 km/h zones all over the dense areas where there are a lot of pedestrians. This is absolutely good, and given traffic and red lights the average speed was less than that anyway -- it's just that now the drivers no longer have that small stretch of road to accelerate to high speeds towards the next red lights.
In the centre, lower speed limits are perfect. Helsinki could've reached zero deaths earlier too if it wasn't for some random truck making a turn and running over a kid or something (I think that was the one traffic death in the previous year, or the one before that).
I'd still like to see fewer square metres allocated for cars, elevated pedestrian crossings, roads with less lanes (you can turn 4 lanes into 3 with bike lanes both ways).