I read up on this awhile ago, it's well described on the 'net.
IIRC not only is SVO (Straight Vegetable Oil as opposed to Biodiesel) difficult to start on, it can leave varnish deposits while cold. Also the SVO needs to be flushed on shutdown- I can't recall if that's because the engine varnishes as it cools down or because the fuel lines will contain SVO running right up to the engine so even if you try to switch the fuel system to normal diesel to get it started there's still SVO in the last part of the lines.
Preheating the lines ensures the SVO will flow in the cold, but it won't get the engine itself up to temp so varnish problems would still be there. Also if you have it gelled in the injector, heating up the line won't thin it there until the SVO starts flowing but it won't start flowing because the gel has clogged it. So ideally you'd need to heat the injector, line, even the bottom of the fuel tank to totally avoid the problem. In the real world, I imagine people still make it work with less than ideal heating systems though.
Also SVO can be of less than consistent quality, such as varying in PH. Some oils can be harmful to the engine. The biodiesel process can adjust for such things.
Biodiesel- or even SVO, IIRC- is actually pretty decent on emissions. OK won't compete with a Prius, but it's supposed to be pretty good.