Many films were made in the 1930's that depicted wealthy people suddenly losing their wealth and having to face lean times with all those others afflicted by the Great Depression. I imagine there were lots of poor people who at least got to fantasize during "Ring Around the Moon" about-- and vicariously experience-- being among the rich and then be gratified to learn that not all the wealthy can stay that way. The interesting thing about this film is that it was made on a depression-era shoestring budget, but has, nonetheless, an earnest, higher-end feeling about it. The acting is sincere and rehearsed with good line-delivery rhythm; seldom does one notice a low-budget, one-take -- whether good or bad-- approach. Donald Cook as Ross, the leading man, could easily have looked sappy or wimpy in this role, but he carries it with about as much dignity as one could.
I found Ann Doran to be impressive and am surprised she wasn't given more opportunities after this appearance to make a name for herself. She has a look in this film much more modern than most other women of her era-- something about her facial structure, her speaking style, and her carriage makes her look more like a woman out of the late 20th Century rather than one from the mid 1930's.
The movie depicts plenty of cigarette smoking, which for some reason doesn't really bother me or distract me from enjoying this film, or any other older film when there is smoking. By contrast, however, smoking in contemporary movies drives me nuts... it is annoying and just looks so affected and egotistical.
In summary, I enjoyed this film very much, as it has a thoughtful and dramatic screenplay (albeit some of the portrayed decisions or actions may seem a bit unlikely in real life, at least in the 21st Century), with the acting and direction earnest and intent on providing a good entertainment...which it does.