I've spent a lot of time adding bridges to the map.
Bridges are important map features since
* They help with routing because it's clear that roads don't intersect.
* They give an idea of how the land appears.
* They explain why there aren't more connections between roads.
That said, I've learned a few things about bridges in OSM.
They are somewhat unusual in they take two tags, bridge=yes and layer=N, where N is 1-5. At first, I thought this was redundant, going as far as to remove layer=1 tags. After all, a bridge implies a higher layer. However, that's not how OSM works.
The layer tag isn't always important for Mapnik to render a good looking map. It seems to understand that a bridge goes above other ways. However, Osmarender needs that layer=1 tag because it gives a priority to each highway= tag. So, for example, a highway=tertiary,bridge=yes way is overwritten by a highway=motorway way. Adding the layer=1 tag to the bridge makes it render properly in both renderers.
So view your favorite area with Osmarender and look for bogus bridges.