I see no problem with this practice of using a prayer box. If anything, I think it shows faith in the power of God to know and understand what his children have written in those sheets of paper. In fact, I like the idea, since it allows for gathering in prayer for those in need, without publishing a gossip section for all to see. It also allows for brevity in payer, which is taught by Jesus in his Sermon on the Mount.
Remember that such prayers are petitions to God, therefore they are intended for God's ears, and not for those in the congregation who are itching for the latest "news" about others. Although the Bible does not state that we should write our requests, it does say that it is not even necessary to voice them out, because God knows what we need even before we open our mouths to pray.
[i]Mt 6:7-8 [color=CC3300]And when you pray, do not keep on babbling like pagans, for they think they will be heard because of their many words. Do not be like them, [b]for your Father knows what you need before you ask him[/b].[/color][/i]