I've heard from a lot of people that LEGO can be washed in the dishwasher, but I'm concerned about warping, losing stickers, wearing off of painted pieces, etc. Is it safe to actually wash them in the dishwasher? Is there any other precaution you should take?
LEGO does not recommend using a dishwasher to clean your bricks:
We recommend that you clean or wash your LEGO parts only by hand at max. 40°C or 104 degrees (F) Fahrenheit. Higher temperatures may affect the quality of the LEGO parts. You can add a mild detergent to the water, followed by rinsing with clear water. Please don't put your bricks in the washing machine or dishwasher or attempt to dry them in ovens, microwaves or with hair dryers. Any electrical parts, such as cables, motors, battery compartments, can only be wiped off with alcohol. Air-dry parts at room temperature. For disinfecting please use mild bleach.
The real answer here is no, but please have a look at my answer to this other question for an alternative that really works, bringing them up as new, with only a little elbow grease - a bath of Milton solution.
I would not recommend using a dishwasher. I have seen terribly worn bricks with a very ugly, dull surface as a result of multiple dishwasher procedures. Sometimes you can notice that a dishwasher etches even a glass surface.
The damage could probably be caused by a combination of the water properties, detergent being used, and temperature.
I have washed thousands of Lego and Duplo bricks in the washing machine as per the suggestion of Lego Store staff that have kid's events. The Lego stores use washing machines. None of by bricks have warped. I use warm water wash on gentle cycle, and I soak them by lifting up the lid. I add about a half cup of chlorine to a load to disinfect the bricks as I have many different kids playing with the bricks.
I purchase washing machine nylon net bags at the dollar store, and put the bricks in the bags. Equipment bags also work well. Do not wash small items that can poke through the netting holes, and especially leaves that get stuck in the small holes of the nylon net bags and rip them apart - those I wash and disinfect in the sink. There are all sorts of strainers available for you to use to fish out the parts from a sink.
I throw Duplo bricks without bags or nets directly into the washing machine, as they are huge, and I shovel them out using a huge draining spoon also purchased at the dollar store. I have over a thousand Duplo bricks and so far not one has been damaged. Stickers are another story. Some are affected, some are not.
Front load washers should be fine with the regular bricks as long as you use the gentle cycle. ABS plastic is tough.
As for dishwashers, they have heating elements that heat the water to a temperature way beyond your water heater. Washing machines never get close to the temperature that dishwashers use. I never saw steam coming out of a washing machine but steam comes out of my dishwasher every time I open the door to it. That is a clue that water is close to the boiling point.
If you are really worried then throw the bricks into a tub full of soapy water and let soak for 3 hours, mix it around, throw in a cup of bleach at the end, drain with strainer over drain hole.