The API reference page https://www.inaturalist.org/pages/api+reference#get-observations indicates that the parameter ‘order_by’ for ‘get observations’ has allowed values ‘observed_on’ and ‘date_added’. In fact it appears ‘date_added’ should actually read ‘created_at’, which is what is used in the other API docs at https://api.inaturalist.org/v1/docs/#!/Observations/get_observations.
I am using pyinaturalist’s get_observations() function, and confusingly, since ‘created_at’ is the default, passing the value ‘date_added’ for the ‘order_by’ parameter does return observations sorted by the date added. However, I am also passing the value ‘asc’ for the parameter ‘order’, and this is ignored when using ‘date_added’ (the results are returned using the default descending order’).
edit: To be clear, get_observations() is now working exactly as I need it, when I use ‘created_at’ instead of ‘date_added’. So, not so much a bug in the API as some confusion in the docs