Excellent posts, construct, but I have to disagree with you on this point. Any case can be persuasive authority. It really is a question of degree. A court of appeals decision is binding (or mandatory) authority on the subject for all courts within its jurisdiction. While a federal district court case is not binding authority, any court can cite it as persuasive authority.
Indeed, US courts sometimes find cases from other countries to be persuasive authority. A perfect example of this is the evolution of the case law regarding employee status verse independent contractor status. The legal concept in American jurisprudence developed during the industrial revolution and was derived from English cases. The English courts developed the law first, and the US imported it here. Of course, the English cases were in no way binding or mandatory, but the courts here found them to be persuasive.
District court cases may have very powerful, persuasive authority in an area of the law that has rarely been litigated and where you have few, if any, Court of Appeals or Supreme Court cases. In an area of the law that has been extensively litigated, and has many Court of Appeals decisions, District Court cases have much less persuasive authority.
Another factor, obviously, is whether the District Court case is published. Now, with extensive electronic research cites like Westlaw and Lexis, lawyers can find unpublished cases. Those would generally have less persuasive authority then a published case.
Federal courts often cite state court cases as persuasive authority where federal courts have yet to weigh in on a subject, or where there is a new federal statute that is similar to a state statute. There, the federal courts import state court precedent to establish federal common law.