Found a workaround: for 0 value data in log scale chart, use cell object {v: 0.01, f:
'0'}. It will still display as 0, but not be evaluated as 0, drawing the line properly.

While it is a nice trick it won't work because it will introduce a distortion in the
chart. 
Bellow I uploaded two files. The first one has {v: 0.01, f: '0'} for 0 values and the
second one has {v: 0.0000000001, f: '0'}.
Space between 0 and 1 is enlarging as v tends to 0. Which is normal logarithmic behaviour
but charts start to look too geeky.

What worked for me was increasing vAxis.gridlines.count to at least 4 in this case,
which made sure that the first vertical line will be drawn for a value greater than
1 (probably for 10 or 100), thereby plotting the 0.01 value together with 0 instead
of somewhere in the air between 0 and 1. 

Also, setting vAxis.maxValue = 1 helps, because then the chart will choose the maximum
plotted value as a higher bound for the vertical axis, leading the chart scale to best
fit the data.

With log scale, the 0 value on the Y axis would be infinitely far down, if scaled 'correctly'.
 So there is no way to include 0 values with a normal log scale axis, and the current
behavior is not really a bug.

However, there is an undocumented feature that might work for you.  You can set the
'scale' to 'mirrorLog', which supports 0 and negative values.  For negative values,
it negates each value, computes the log of that, and puts the negative back on.  For
values close to zero, positive and negative, it uses a linear scale. 

I'm sorry. Could you please tell where property scale should be placed?
My options object looks like:
var options = {
    pointSize: 5,
    //interpolateNulls:true,
    vAxis: {
        logScale: true,
        format:'#,###,###',
        gridlines: {count:3},
        minValue : 0,
        baseline : 0
    },

    hAxis: {
        format: 'dd.MM.yyyy',
        maxValue: new Date('03/11/2013'),
        minValue: new Date('04/03/2013'),
        viewWindowMode: 'pretty' 
    }
};
I tried to put scale attribute in options and in vAxis object. Ex: scale:'mirrorLog'
but I didn't see any effect.
Version of visualization package is:
  google.load('visualization', '1', { 'packages': ['corechart'], language:'RU' });

Thank you very much!

Sorry, I forgot that the option name was changed as well.  Instead of logScale: true,
use "scaleType": "mirrorLog".