User can't type '.' in the textbox that have been bound to a float value while UpdateSourceTrigger is PropertyChanged in WPF

Maybe it would help if you add a StringFormat statement in your binding:

<TextBox
    Text="{Binding Amount, StringFormat='{}{##.##}', UpdateSourceTrigger=PropertyChanged}"/>    

Update: I saw that my first answer throws some binding errors..

An other option is working with a converter (works, but a bit dirty ;-) ):

...
<Window.Resources>        
    <local:FloatConverter x:Key="FloatConverter" />
</Window.Resources>
...
<TextBox Text="{Binding Amount, UpdateSourceTrigger=PropertyChanged, Converter={StaticResource FloatConverter}}"></TextBox>

Converter:

public class FloatConverter : IValueConverter
{
  public object Convert(object value, Type targetType, object parameter, CultureInfo culture)
  {
     return value;
  }

  public object ConvertBack(object value, Type targetType, object parameter, CultureInfo culture)
  {
     // return an invalid value in case of the value ends with a point
     return value.ToString().EndsWith(".") ? "." : value;
  }

}