Giving mirrored film (available at art-supply stores) even a subtle curve will provide a fun-house-like distorted reflection: You might look upside down when standing up close, very tiny when standing back a few feet, and so on. This project is simplest with a rectangular mirror frame.
Remove the original mirror from the frame. Flip the frame over, and place it on a piece of poster board or corrugated cardboard. Trace the opening of the frame onto the board, adding 1/4 inch to the top edge; cut out with scissors.
Coat the smooth side of the board with super spray adhesive, and adhere a 2-mm-thick sheet of mirrored film to it. Trim any excess film around the edges of the board. Apply a thin strip of hot glue to the inner lip at the top of the frame; secure one edge of the mirrored board to the lip. Repeat process on bottom lip. This will create a slight concave curve in the mirror, since the board will be larger than your frame.
The curve in the mirror will leave small gaps between the mirror and the sides of the frame. Cut pieces of cardboard in the shape of these gaps and cover them with mirrored film. Using hot glue, attach the pieces to the mirror and frame, plugging the gaps.
Hang mirror as usual.