Do you mean which projects the user is allowed to see problems? If so, you want to use
getPermissionSchemes to retrieve the RemotePermissionSchemes array, then use getPermissionMappings for each of them to get the permissions you want to see, for example. View problems (by id). The problem is that you have to do this for all projects (you can cache), but then getting the role for the user will work only for the registered user.
summary: I would write my own SOAP method to do this
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