A federal judge ordered The Washington Post yesterday to show cause why it should not be held in contempt of court for allegedly failing to comply with his order requiring the newspaper to arbitrate grievances brought by the Washington-Baltimore Newspaper Guild.

Local 35 of the union, which represents editorial and commercial employes at The Post, has claimed that despite a 1977 order by U.S. District Court Judge John H. Pratt, the newspaper has refused to arbitrate all the grievances that have been filed by Local 35 against the paper's management.

Lawrence Wallace, the newspaper's vice president for labor relations, said that Pratt had ordered the company to arbitrate four specific grievances and that The Post had done so. In addition, the company is arbitrating four other personnel disputes, Wallace said.

But the union has claimed that The Post should also be required to arbitrate grievances over a payroll checkoff for union dues, a union security clause, a cost-of-living pay dispute and company contributions to a health and welfare fund for workers. The overall issue centers on whether provisions of a now-expired contract the union had with the company remain in effect while a new contract is negotiated.

The union's lawyer, Alan D. Eisenberg, has asked Pratt to fine the company $10,000 for each violation of the judge's 1977 order and $1,000 for each day that the violations continue.