When a new Interactive project is created, the colors available in the color palette are default CMYK colors. Since SWF is a screen format , CMYK colors dont convert very well in the exported swf.
This is the reason why text or drop shadows that use the default black color look different in the exported swf.
To get best results it is advised that you use only RGB colors in the interactive layouts. For this go to Edit Colors -> and create new colors. In the model drop down select RGB and then create your new color.
Create a RGB black color by giving 0 value toR, G and B and use this for black text and drop shadows and notice the improvement in color reproduction in the exported SWfs.