well, you would get the same effect if you build a spaceship that can traverse the universe at a faster than light speed (I personally prefer the theories that fold space, but yeah, that is still very sci-fi until science understands it better).

Wherever your FTL spceship ends up, if it would look back at earth (with a very good telescope), it would see into the past, the further it traveled FTL, the further in the past it would see.

Assuming the optics could be worked out, as others have mentioned the various problems, to see to our past, the mirror would have to already exist, and would have to have existed at a time T/2 for whatever time T you want to look back in time. If you wanted to see some dinosaurs walking the earth, an appropriately impossible mirror would have to have been put in place, over 150 million light years away, over 150 million years ago.

If you were to put a mirror out in space today, you could not see to any time prior to today. This is just basic geometry. Not assuming faster-than-light travel, if it takes M years to place a mirror N light-years away, with M greater than N, then in M years you could look back in time to a point in our current future. The effect would be such that, if we watched the mirror continuously as it were flying away, it would show us a "live video stream" from the day we launched it, in slow motion, and then in M years when it finally reaches its destination, the slow-motion ends and the "video stream" will resume to normal speed, offset from our own timeline by 2N years.

As it turns out, a similar reasoning applies to why time machines will never be created to allow us to travel back to any time prior to when the time machine was created. Any such time machine would require faster-than-light-speeds-without-space-folding. And I've been assured by people who have studied the issue much more than I have that such a thing is impossible.

Nahh, the light would have to bounce off of something really distant for that to work, which it probably wouldn't. Something like a really big shiny planet might do but what planet is shiny? None. I don't think its possible.