Data or routing algorithm glitches

Zoom in at the 8 and 9 pins in http://cycle.travel/map/journey/10597

You see that the route takes a detour into the town to the south of the channel 8 and 9 are located on. There is a bicycle road along the channel between 8 and 9. If I drag the route from the town to it, the route follows the channel up to the bridge past the town, then goes back on itself and into the town. I don't know if the bridge is marked as impassable from north to south (S to N is OK) or it's the routing algorithm that can't deal with it.

There is a problem with a roundabout between the pins 15 and 16 and also the bicycle bridge over the road (move 15 and 16 over the bicycle road). Again, it's either the data or the algorithm. My bet is on the data in both cases.

I'm not familiar with OSM and I don't know how to check if the data are right. Could anybody point me to a tutorial explaining how I can inspect the data and fix it if it's wrong? I don't expect it to be easy, but I'm genuinely interested. Thanks.