The following are some indications you can look for to tell what mode the application is running in:

Classic Mode applications

• The apple menu in the left hand corner will be multi-colored.
• The name or icon of the application will appear in the upper right hand corner of the menu bar.
• Windows for classic applications will have the a close box in the upper left hand corner and a window shade and resize box in the right hand corner

Native applications

• The apple menu in the left hand corner will be blue.
• Windows will have three colored "stones" (red, yellow and green) in the upper left hand corner