R.D.
I got one of those 'baskets' for the dishwasher (they're like $3 or $4 from Target) for all the nipples and rings and things for the bottles, and yes, I put EVERYTHING in the dishwasher!! Of course it cleans and sterilizes, would you eat off the plates you put in the dishwasher if they weren't coming out clean?
Gone are the days of boiling bottles and using bottle sterilizers (the latter being a complete joke and marketing scam to begin with). Out of 3 kids, NONE of them had any issues with me putting bottles in the dishwasher. In fact, it's been proven that there are more instances of thrush from poorly hand washed bottles. My kids never had thrush or anything else due to the way I washed the bottles... in the dishwasher ;)
You're going to want to trash any old nipples though, because they can dry rot and break apart in babies mouth. Buy all new nipples.