I've seen a lot of widdershins roundabouting by the Strava route planner, which I attributed to USAnian developers not understanding a) what a roundabout was or b) that we ride on the left side of the road.
A bigger issue is that it has no clear understanding of whether a given track is cycleable or a footpath. I accept that that's an NP-hard problem, and the mapping will always have inaccuracies, but it seems particularly bad at sending you on a helpful shortcut over a stile and through a muddy field with a 25% gradient and wandering cows when there's a perfectly good road route that's 100m longer.
But the tiles thing is handy. I use the route as a guide for plotting in Basecamp (or if there's non-trivial off-road, it gets tidied up in ridewithgps), so I tend to discover most of this from the comfort of my computer.