I have a style on my WPF Tooltip which basically makes it look like a speech bubble. The pointy part of the bubble stops aligning properly when the control is to the right o
Standard WPF Windows 7 style

The standard WPF tooltip positions at the mouse pointer, which look perfect in my opinion.
The picture below illustrates your problem

If you really want to do what you are asking, it is possible: you need code-behind on the style to calculate the horizontal adjustment, put this into ToolTip.Tag, and bind the pointy part border to the calculated adjustment:
Revised ToolTip style -
Code-behind
private void ToolTipOpenedHandler(object sender, RoutedEventArgs e)
{
ToolTip toolTip = (ToolTip) sender;
UIElement target = toolTip.PlacementTarget;
Point adjust = target.TranslatePoint(new Point(8, 0), toolTip);
toolTip.Tag = new Thickness(adjust.X, 0, 0, -1.5);
}
This answers your question as asked,

but is not sufficient when tooltip is near the bottom of the screen:

To fix this you can amend the code-behind to detect that the tooltip is above the target and set the tooltip Position to Top, and a Property Trigger style the tooltip with the pointy part below the rectangle -
Complete XAML (includes wide, narrow and multi-line tooptips)
TopLeft
TopRight
CenterLeft
CenterRight
Multi-line ToolTip for Bottomleft - MMMMMMMMMWWWWWWWWWW x y z
BottomRight
Code-behind
private void ToolTipOpenedHandler(object sender, RoutedEventArgs e)
{
ToolTip toolTip = (ToolTip)sender;
UIElement target = toolTip.PlacementTarget;
Point adjust = target.TranslatePoint(new Point(8, 0), toolTip);
if (adjust.Y > 0)
{
toolTip.Placement = PlacementMode.Top;
}
toolTip.Tag = new Thickness(adjust.X, -1.5, 0, -1.5);
}
Final result


The pointy part now adjusts horizontally when tooltip is near the right of the screen, and vertically when tooltip is near the bottom of the screen.