No difference between single coated and multi coated filters/lenses. Cheap filter may have no coating , so check first. If a cheap filter has some colour reflection when you look at it at an agle, it has coating and is good enough, no difference with more expensive ones. CKiang is right that some cheap filters are made from plastic, avoid those as they warp over time. As long as they are glass and at least soingle coated they are as good as expensive ones! Don't get entangled in the marketing strategy of companies that makes you to believe 15 layer coating is better than 5 layers or 1 layer. The differences are there only under lab conditions, not in real life.
Some polarisers, even more expensive ones (like heliopan) has some colour casts (green), so there is no guarantee that when you buy expensive ones it is going to be good.......save money for films (or memory cards)