I very much doubt that there will be a next level. As I understand it an appeal does not introduce new testimony or facts. The current judges decides the facts. What would there basis be for appeal?
It will be strictly based on legal issues -- specifically, whether the facts, as the judge finds them, mean that the school board's actions violated the First Amendment. The currently prevailing case on this is LEMON v. KURTZMAN, 403 U.S. 602 (1971).
I've posted this a few weeks ago, but it's relevant now that the case is winding up.
That case lays out the three-pronged "Lemon test":
First, the statute [or state action] must have a secular legislative purpose;second, its principal or primary effect must be one that neither advances nor inhibits religion,
finally, the statute must not foster "an excessive government entanglement with religion."
Is there anyone who imagines that the mandatory ID statement which the Dover school board imposed on the schools can pass that test? (Don't get hung up on the word "statute." The school board's mandate undoubtedly qualifies as "state action" under the 14th Amendment.)
By the way, in Selman v. Cobb County School District, the Georgia textbook sticker case, the court cited and relied on the Lemon test. But there's a bit of Supreme Court politics involved here. In Tangipahoa Parish Board of Education v. Freiler, a creationism case where the Supreme Court denied certiorari (in 2000, only 5 years ago), Rehnquist, Scalia & Thomas indicated that they'd like to re-visit the Lemon test. So it's going to be a long and bumpy ride.
What would there basis be for appeal?
I'm not a lawyer, but I don't think the perjurors are dumb enough to present their perjury to review by a higher court. But I could be wrong.
I think the DASD wants to go home and forget this ever happened.