I guess this answer really depends on the motivation of you, the parent. If you are trying to see their profile to "spy" on them by calling yourself someone esle or something like that, then no. If that is the case, you should really talk to your child, because if they ever find out what you did, it will broaden any gap between you.But, if you are trying to be close to your child, and they are ok with that, then go ahead. As far as a limited profile, you wont see a lot of things like some wall posts or pictures ( which is the bulk of the content parents are interested in).While my parents arent my Facebook friends, they are friends with me (im 22) and my little brother (16) on MySpace , and he doesnt have Facebook. Our parents trust both of us, and we have a great relationship!
Hope that helps....