The written judgement is already available; it's a five-page document containing the decision by the appeals court (reversal of the verdict in the lower court), the claims of both the complainant-defendant and the prosecutor, the basis for the judgement (presentation of original evidence and arguments by both parties), and finally the court's reasoning, which I believe is what you are most interested in (and which I have translated below). The crucial issue was not about interpreting the Swedish Copyright Act, but a matter of evidence in this particular case.
The lower court has, in its understanding of the sequence of events, emphasized the information allegedly provided by [the defendant] in the interrogation, and ruled out the possibility of evidence manipulation that has been alleged by the defense.
Before the appeals court, [the interrogator] has changed his statement and stated that in the case that the movie Hip Hip Hora is not mentioned in the interrogation records, he has never asked questions about that particular movie. The appeals court therefore finds that from the information provided by [the defendant] in the interrogation, he cannot be considered to have previously admitted that he has made the movie Hip Hip Hora available or that he has had it in his possession.
[The expert witness] has explained that, among other things, securing evidence, verification of time zones and knowledge about the user's computer, firewalls or routers is essential information that must be included in an investigation of copyright infringement. If this is not the case, then there are multiple sources of error in the process of establishing the identity of a user. [The investigator] has stated that the timestamp in the CommView report together with the information from Bredbandsbolaget is sufficient to conclude that the download was made from [the defendant's] computer.
In order to find [the defendant] responsible for the action he has been charged with by the prosecution, it must be shown that the IP address mentioned in the investigation has been assigned to computer equipment belonging to or being used by [the defendant], and that nobody else could have been using said equipment at the time in question.
The investigation does not further detail what computer equipment [the defendant] had access to at the time in question.
The appeals court has found no reason to believe that [the defendant] has provided incorrect information in this case. The prosecution has however not claimed that the timestamp in the CommView report has been verified. What has been established primarily through the interrogation of [?] means that no certain conclusion can be drawn regarding the time when the movie was transferred, and therefore neither that the transfer was made from [the defendant's] computer equipment. The charges are therefore to be disapproved.
The decision was signed by three judges, and was unanimous. The prosecution has until October 30, 2006, to file a request to bring the case before the Supreme Court of Sweden (a highly unlikely filing, in my opinion).