In fact it has always been known that this model is wrong when you describe it classicaly, this is because moving charge emits an electromagnetic wave which drags energy out of the system. You can calculate how much time it has before the electron falls into the nucleus and its, as far as I can remember, less than a second. So yes, it contradicts classical electrodynamics. Bohr knew about that problem.
The thing is that the Bohr model was successfully describing the discrete energy lines of quicksilver with high accuracy, something which other models were not able to do, so there has to be some truth to it (and there is, namely the quantization of angular momentum and the probabilistic interpretation of quantum mechanics which give discrete energy levels).

There are many more problems with this model:
1. emission of electromagnetic energy
2. atoms are not "flat": conservation of angular momentom suggests flat orbits, though
3. angular momentum of the ground state is in fact zero, so there is no orbital movement
4. it contradicts Heisenberg's uncertainty principle: you cannot know momentum and position to an arbitrary high precision; alternatively you cannot know the complete angular momentum vector.


I've once read a physics book when I was... dunno... fourteen or so.