There's no question that many of the downloads available from The Pirate Bay are for files that certainly infringe copyrights. The question is whether they're responsible for that content. One defendant has called that idea "idiotic."
Another key point of contention is the possible influence of Warner Brothers on the case. Last April it was revealed that the prosecution's star witness took a job with the US based entertainment giant shortly after charges were filed in Sweden. The Pirate Bay is also being sued by the MPAA over a number of movie and TV downloads, including two Warner Brothers releases.
Sweden isn't the only place The Pirate Bay is involved in a dispute with government officials either. Just last September they won a major victory when a prosecutor's decree requiring ISP's to block their website was reversed on appeal.