My only massive problem is letting them into the run when it is muddy and wet, Because of their long fluffy hair you can imaging the mess, therefore i let them onto the slabs and still brush them daily.
I've never had them eating their own young, but then again none of mine are novice,
I have more of a problem with younger, flightier rabbits such as my dutch ones eating their offspring. Apparently it is to do with lack of minerals (or something like that not exactly sure,but I'm sure thats what the vets said) so ours have extra daily suplaments that seem to do the trick,
Also as with all pregnant animals and young keep them separate and makesure that you have another spare hutch for the baby boys, as they can breed at about 4/5 weeks old!
Hopefully this is a bit more enlightening
Cameron