WASHINGTON — The 35-page dossier, spiced up with tales of prostitutes and spies, sketched out a hair-raising story more than two years ago. Russian intelligence had used bribery and blackmail to try to turn Donald J. Trump into a source and ally, it said, and the Kremlin was running some Trump campaign aides practically as agents.

But the release on Thursday of the report by the special counsel, Robert S. Mueller III, underscored what had grown clearer for months — that while many Trump aides had welcomed contacts with the Russians, some of the most sensational claims in the dossier appeared to be false, and others were impossible to prove. Mr. Mueller’s report contained over a dozen passing references to the document’s claims but no overall assessment of why so much did not check out.

Now the dossier — financed by Hillary Clinton’s campaign and the Democratic National Committee, and compiled by the former British intelligence agent Christopher Steele — is likely to face new, possibly harsh scrutiny from multiple inquiries.

Republicans in Congress have vowed to investigate. The Justice Department’s inspector general is considering whether the Federal Bureau of Investigation improperly relied on the dossier in applying to the secret Foreign Intelligence Surveillance Court for a warrant to eavesdrop on Carter Page, a Trump adviser. The inspector general wants to know what the F.B.I. learned about Mr. Steele’s sources and whether it disclosed any doubts about their veracity to the court.