My old dog gave me a real scare and had his leg go in between some slats on a really steep ramp. I thought for sure his knee was gonna be screwed but it ended up ok.
Years ago, I can remember a dog jumping off of a bridge at the woodlot and getting its leg caught and getting hung up really good. Once again, I think the dog ended up ok but it looked super bad.
We try to deter our dog from going on bridges, but in the end let him use his own judgment. While large spaces between slates can be an issue, it is also that some bridges end in drops or steep roll downs that can be an issue for the dog, so they try and turn around and go back. If someone happens to be following the dog this can also cause them to panic.
As a builder, I try to make all my bridges as though a dog will end up on them at some point. I can likely be faulted for putting the slates too close together but so far I don't see any issues with the bridges durability in doing so.