Additionally, there is no visual indication that you've beaten your best time (whereas you would see A+ show up on the screen when you first get under the par time).
When you beat your best time, a little grey bandage girl flashes for a second in the bottom left corner of the screen.
It would be nice to see your best time on the screen though.
Oh right, forgot about that one.
However, it's hardly noticeable and the eye is not naturally drawn to the bottom corner. Generally, the eyes are focusing on the center of the screen -- where Dr. Fetus takes Bandage Girl (or Meat Boy for Cotton Alley) away, the "Bandage Get" notification is, as well as the "A+" notification.