From my own observations I think that a lot of the time there is little difference between the results obtained using uncoated filters, single coated and multi-coated, but there are some lighting situations where there is a difference. Because of that I go for multi coating if it is available and doesn't have too much of a price penalty, otherwise I don't worry too much.

B+W seem to have improved their multi-coating quality over the years - so beware of older filters and stick to the current 'MRC' multi-coating. My earlier B+W 'MC' filters have softer coating than my Hoya 'HMC' ones.

As far as I know, there are few square filters that have multi-coating. I use B+W/Schneider, and there aren't many of them available with multi-coating. Some are available with single coating, and some uncoated. The fact that square systems are popular suggests that a lot of people manage quite well with uncoated filters. It's more important to use a lens hood, and to protect the edges of the unmounted square filters from stray light.

Best,
Helen