What would the world look like if we could detect the polarization of light?
For one, we might be better at navigation:
Polarized light is produced a variety of ways in nature. The atmosphere and water both refract un-polarized sunlight, producing a polarized light pattern. This creates a striking pattern in the sky that many animals use as a navigational compass.
As far as how we would interpret colors and such if we could see polarized light, you need to understand that polarization is different than other colors. For human color vision, we have cone cells that are particularly stimulated by certain wavelengths of light. For instance, blue-detecting cones are most stimulated by light with a wavelength of around 430 nm. Polarization is basically which direction the light wave is vibrating. This is independent of wavelength - you can have blue light polarized the same as red light, while another source of blue light could be polarized differently than those two.
Given that wavelength and polarization are independent, I think we would interpret it separately. For comparison, think about light blue, light red, dark blue, and dark red. The darkness or lightness of the color is easily separated from the color itself. Polarization would be like that - another aspect of color that we would be able to describe and that can easily be compared across colors.
What magic tricks, etc. would no longer work on us?
This wouldn't prevent any magic tricks from working on us. When was the last time you saw a magician do a trick that was actually obvious because some part of the trick accidentally used two different colors when it should have used one? Being able to perceive polarized light, the magician would make sure that the materials used didn't polarize light in such a way as to give the trick away. It's entirely possible that magicians would have to be more particular about lighting and materials used, but that's not a significant change from what they do now.
What would no longer be hidden from us?
Some animals use polarized light as part of their mating routines, so we would be able to see them wooing each other.
What would be obfuscated?
Nothing natural. You'd have to design something that rapidly changed the polarization of light it reflects/emits to produce a strobe-like effect. As I said earlier, polarization would be categorized differently than color, so it would not make it harder for us to perceive anything that we can currently perceive.
How would we perceive the sky and the stars?
As I quoted earlier, the atmosphere polarizes light from the sun, so we'd be able to see patterns in the sky that could help us navigate. Stars produce unpolarized light, so they'd look the same other than how the sky polarizes light.