At the moment, casual observations do not show up on the observations map; nor do they appear on the map in the explore mode.
I often use the explore feature to observe the distribution of species across the landscape; I would wish to see individuals, regardless of if they are casual or not, in order to get a better portrait of the presence and absence of species; for research projects and science in general, this would be useful.
I often refer to either my observations or the explore feature to focus new informal surveying in zones where there are no observations, but excluding casual observations biases this, as there may be several observations which simply do not appear.
The simplest way to achieve such a result would be to have the option to filter in/out casual observations in the search filters.
They’re two slightly different results (the first will exclude obs with things checked in the Data Quality Assessment) but either or both should get what you’re looking for I think?
It sound like your topic is posed as a feature request though, so if there is functionality not already present on iNat that you’re hoping to be added please use the Feature Requests category.
You can see casual observations in explore. I am not sure whether you can see all casual observations this way - but you can at least see all that are casual because they don’t have a photo or sound - just uncheck “verifiable” in “filters”.
I use this a lot, it’s super important for researching plant species that tend to escape from landscaping, because I often want to look at the relationship between where a plant is planted in landscaping, and where it escapes into the wild. iNaturalist currently actually makes it fairly easy to find this data if you know how to filter for it.
It takes a little fidgeting, it’s a bit complex because certain boxes tend to be exclusive with others, like research grade requires something be verifiable and wild, and wild and captive are mutually exclusive.