I don't know a lot about biodiesel really, but there are a couple of points that spring immediately to mind.
One is that a lot of biodiesel is made from crops that are not overly sustainable, like soy which is being farmed on huge scale as a monocrop in places like Brazil, where they are busy cutting down rainforests to plant more of it. Of course that's probably still better than digging up and burning huge amounts of fossil fuels, but it's still far from ideal.
It can be made from a lot of other sources though, different kinds of hydrotreated vegetable oil, including waste products.
The other point is that it has one of the same big problems as hydrogen, which is actually finding somewhere to buy it. I don't think I have ever seen a fuel station selling biodiesel anywhere that I have lived. I did read somewhere that it is pretty common in Finland though, with the fuel company Neste there producing a lot of it. Maybe it will become more common across the rest of Europe as well.