The submission processes should do as much as it can to inform authors of new petitions of these issues to ensure that they don't feel misled by the opportunity presented by this platform.
A good example of a platform that does this is Quora, though Uservoice and Get Satisfaction does some of this as well. These platforms analyze the text of new entries before they're submitted to see if similar entries already exist. Some, like Quora, also do additional analysis to look for key words and correct question and grammar structure to help ensure that submissions are worded in a way that meets the intent and quality standards of the platform. If they're not, it helps guide the user through better wording.
A similar process could be used to look for entries that don't meet the Terms of Service for We The People, but I think the larger strategy of helping to phrase petitions correctly is also very important.