Corrected entry: Mr Bobinsky is supposedly Russian (he calls the new cheese "novy syr", the mice "myschka" etc.), still the flag hanging from his window is Macedonian (a two-headed eagle on red). He might be royalist, however the traditional standard of the Russian Tzars is a two-headed eagle on golden background.
Correction: Displaying a Montenegrin flag doesn't mean he's Montenegrin. There's no reason why someone could not be displaying another country's flag at their home. In Canada, I have seen numerous flags flown at people's homes including British, French, German, Russian, etc. It doesn't necessarily mean the people flying the flags are from that country. Bobinsky can be Russian, but may choose to display the Montenegrin flag if his family, or he, were originally from Montenegro, for example.
Revealing mistake: In the scene where Coraline is in the garden in the other world looking for the ghost eye, she looks through the magical seeing stone and spots the other father on his mechanical praying mantis tractor. When he arrives at the bridge, and it snaps, he breaks off the ghost eye from the gear stick and then he collapses through the bridge into the water. But if you look closely, he is slipping through what looks like some black material, not real water. (01:01:25)
Suggested correction: It's the other world, it'll probably not have real water. It makes more sense to be a black substance.
Correction: It's not a Montenegrin flag, but a Russian coat of arms.