These shows cannot harm children if the children understand that much of these reality setups are indeed, set up. Also, they should recognize that it is a mere television show and need to understand that television is for entertainment. The stuff that happens on TV should not be harmful to children.
I think that they are pretty good shows for helping out the kids. I think that they can teach kids that they need to be competitive, and that they can be really good motivators for kids to want to go and do some fun things they saw on the show.
Competitive reality shows, particularly competitive reality dating shows such as The Bachelor, send harmful messages to children. The producing and editing of these shows reduce real people to their most base and stereotypical qualities, often glorifying bad behavior. This is then presented as reality to children who have soft little developing brains that can't differentiate this from normal behavior, so it's harmful.
I believe that competition-based reality shows are harmful to children due to encouraging a more "mean-spirited" competitiveness. Additionally, certain behaviors taken by contestants would normally be frowned upon by society in general. For example, on the show Big Brother, it is common practice to spread rumors about other contestants in order to not only establish a person's place in the game, but to also destroy another contestant's reputation. On some other shows, contestants can get together and form alliances (or cliques) to establish a social hierarchy over other contestants, and is encouraged. Some players may also resort to dirty tactics (without blatantly cheating) in order to gain an advantage. Since children do like to emulate what they see on television, they may repeat these behaviors with negative repercussions.
I do not believe competitive reality shows are helpful or harmful to children. Competitive reality shows could be a lot of different programs but I would say the most common would be shows such as the The Bachelor(ette), Big Brother, and Survivor. While some of these shows may be watched by children I don't think they comprehend the interactions between participants which is really what the shows are about. Generally, I would say there is far better programming for children rather than this.