Guess the problem is here:

https://github.com/piwik/piwik/blob/master/plugins/Live/API.php#L308

If period is day it will always show the day before!

PLease also refer to [http://forum.piwik.org/read.php?5,76195] - I already had a talk with Matt about this statement. It seems like deleting the "->subDay(1)" call would rise another issue.

I have commmitted a patch for this issue, see the few lines following: https://github.com/piwik/piwik/blob/master/plugins/Live/API.php#L372

I haven't tested much, in particular with timezones like GMT-8 and GMT+8 but these few lines should help

(In [4710]) Fixes #2387 - test is most welcome!

Thanks for the fix, but I'd like to know if it is ok just overwrite the stock file(API.php) with the trunk.

In stock 1.4, the "->subday(1)" makes errors on day/week/month/year selection on specific dates in Visitor Log page, please check my test result on (note: user-defined range does not have errors)
http://forum.piwik.org/read.php?2,76196,page=1#msg-77084

It's not going to work to reuse the API.php file like this, but you can just try to change the IF block that starts at line: https://github.com/piwik/piwik/blob/master/plugins/Live/API.php?rev=4710#L375 then it should work with 1.4

Your tests are very appreciated.. I am not 100% sure that all issues are fixed!

so far so good it seems to have fixed my issues will report back if I find anything.