I discovered this error in my statistics and i checked it twice in piwik demo and yes… there is an error too in piwik demo.
In visitors tab when you change the range to day by clicking in the last day of a month (select previous month or 3/4 months ago) what you get is the statistics for that day and all the previous days in that particular month.
After export those values in a CSV sheet you can see the total sum for those values (for the whole month) and I think there is an error in unique visitor value. Those totals have to be exactly the same than the totals of the month… but ohhh surprise!.. only unique visitor total value is not the same.
If you open the attached file you can see that the real total for the unique visitors is 20658 but in the statistic range by month is 17013.
Hope this helps.
Congratulations for the project!