Most thin sheets of polyester actually function as retarders (not necessarily quarter wave plates) due to the way their molecules are aligned during manufacturing. Here's one of the better cites on the topic, it includes some math to design any desired retarder:

http://arxiv.org/pdf/physics/0702225.pdf

Using a linear polarizer does change the polarization. If he puts his polarizer halfway between the incident angle and the desired angle, he'll get cos⁴(theta/2) of the original intensity in the desired polarization.

If you have two perpendicular polarizers, no light will pass through both. But, if you insert a polarizer at a 45 degree angle to both of them inbetween, some light will pass through. Am I wrong?

You are exactly right.

This is why I trawl the comment section.