Qualcomm Corp. has started a fight with its own lawyers and IT consultants over one of the thorniest questions about legal discovery in the electronic age: Who’s responsible when a company fails to turn over electronically stored information?

The dispute is unfolding in federal court in San Diego, Calif., where Qualcomm has been embroiled in patent litigation against its rival Broadcom Corp. Then came the revelation that Qualcomm failed to turn over what were deemed to be critical e-mail messages in that dispute. A federal judge fined Qualcomm—and, to the surprise of many, recommended disciplinary action against several of its outside attorneys.