I am unable, at this moment, to set up 2.0beta and perform these tests. I can report back with my findings when I am able to do so. In the meantime, I ran the tests from piwik.org....
Here is an example using the Piwik.org API reference URLs and data ->
http://demo.piwik.org/?module=API&method=UserCountry.getCity&idSite=3&period=range&date=2013-10-01,2013-10-31&format=xml&token_auth=anonymous
For October 1st to the 31st, for 'Unknown city', the API reports 252 visits and 248 sum daily unique visitors. That's look correct.
Now set the start date for that range back one day into the previous month....
http://demo.piwik.org/?module=API&method=UserCountry.getCity&idSite=3&period=range&date=2013-09-30,2013-10-31&format=xml&token_auth=anonymous
For September 30th to October 31st (one day more than the previous range), for 'Unknown city', the API reports 260 visits, but only 31 sum daily unique visitors.
This error exists for all cities in the results, and the same in the regions and countries reports as well.
Here is an example using the Piwik.org API reference URLs and data ->
http://demo.piwik.org/?module=API&method=UserCountry.getCity&idSite=3&period=range&date=2013-10-01,2013-10-31&format=xml&token_auth=anonymous
For October 1st to the 31st, for 'Unknown city', the API reports 252 visits and 248 sum daily unique visitors. That's look correct.
Now set the start date for that range back one day into the previous month....
http://demo.piwik.org/?module=API&method=UserCountry.getCity&idSite=3&period=range&date=2013-09-30,2013-10-31&format=xml&token_auth=anonymous
For September 30th to October 31st (one day more than the previous range), for 'Unknown city', the API reports 260 visits, but only 31 sum daily unique visitors.
This error exists for all cities in the results, and the same in the regions and countries reports as well.