Trash in space as a solution of our trash problem is VERY expensive. It would cost about a million dollars to put a ton of garbage in earth orbit. On the other hand MARBORG industries charges about 100 dollars to remove a ton of trash.

Far as what would happen to it...well the trash would go into orbit around earth traveling at 8 km/second; it would be cold when in the earths shadow and hot when in sunlight... but other than that not much would happen... well it would change chemically due to heating/cooling...