My kids' kindy and pre-primary classes (not sure what the equivalent is for you over east - they're 4 and 5 yrs old) are always hectic with mobs of kids doing different things at different activity tables, but things are done in sessions and everything is put away neatly once that particular session is finished. It never looks worse than organised chaos ITMS, and I've never thought whoa, they've lost control.
The sick room is a room I would expect to always be tidy, unless a child has literally just left.
Like Tan said, the teachers are well dressed - I've seen them wearing jeans but always tidy with dressier tops etc. I think its setting a pretty bad example for the kids if they come in looking like they've just rolled out of bed after a heavy night!
And even if all of that is maybe a bit much to expect all the time, if your gut has you doubting its the place for your little girl I think that's probably a good enough reason to cross it off your list and keep looking.