For West German authorities who were braced for serious trouble as more than 500,000 people massed for peace protests during the Easter weekend, the toll was remarkably benign: one man bitten by a dog, one canister of tear gas used to disperse marchers at a U.S. Army base and a few minor arrests in West Berlin.

Yet the placid nature of the first spring demonstrations against the prospect of stationing new nuclear missiles in Western Europe later this year may prove deceptive, because ominous challenges loom for the government of Chancellor Helmut Kohl.

Peace activists warned that the four-day series of about 90 marches was only the "last rehearsal" for more serious actions in the summer and fall to prevent the deployment of Pershing II missiles on West German soil.

Moreover, the opposition Social Democrats' staunch endorsement of the Easter protests provided another indication that they are prepared to break with traditional consensus on defense matters and fight the government over the missiles issue.

Social Democratic spokesman Wolfgang Clement bitterly denounced as "a sign of political helplessness" the government's condemnation of the West German peace movement as being "communist-infiltrated" and "a tool of Soviet policy."

A senior Chancellery aide, Phillip Jenninger, in turn criticized the opposition party's call to join the anti-missile marches as tantamount to "the withdrawal of the Social Democrats from a common security, defense and foreign policies."

Conscious of the dangers to West German unity posed by the missile debate, Kohl has taken the lead among the allies since his election March 6 to urge a more active U.S. search for compromise in Geneva negotiations on medium-range nuclear weapons.

His spokesman announced last week that Kohl and Foreign Minister Hans-Dietrich Genscher will travel to Washington April 14 for a one-day working visit with President Reagan to discuss the coming Williamsburg economic summit as well as the the Geneva arms talks, which are to resume next month.

Kohl is known to be deeply worried by the many economic disputes between Europe and the United States over such issues as farm subsidies, high interest rates and East-West trade at a time when the alliance will undergo severe strains from protests over deployment of nuclear missiles. His efforts to bridge those rifts seem likely to be complicated not only by the vehemence of Reagan administration demands on the economic issues, but also by the widening breach between his government and the Social Democrats on security matters.

Since their resounding defeat in the March election, Social Democratic moderates have continued to lose their influence. Former chancellor Helmut Schmidt intends to drop out of the party leadership, and Egon Franke is still embroiled in a scandal over missing funds during his years as interior minister.

The growing tensions about missile deployment have emboldened shrill voices on the left wing of the party. At an Easter weekend rally in Duisburg, Oskar Lafontaine, a member of the Social Democrats' executive board, decried U.S. nuclear strategy as "absolute insanity" and urged resistance against attempts "to turn our country into the nuclear battlefield of the superpowers."

Alluding to what he said is the more imminent threat of nuclear war if the Pershing II missiles are installed, Lafontaine also charged that West Germany's membership in the North Atlantic Treaty Organization is no longer acceptable if "we are placed on a powder keg while the match is being ignited."

While top party officials disowned suggestions that West Germany should leave NATO, the Social Democrats have, in effect, repudiated the 1979 NATO two-track decision--calling for missile deployment this year if the Geneva arms talks fail--that Schmidt's government largely instigated. Hans-Jochen Vogel, the party's unsuccessful candidate for chancellor and now its parliamentary leader, has backed a proposal by one of his deputies, Horst Ehmke, that rules out deployment of Pershing II missiles in West Germany and restricts any future deployment to the slower cruise missiles that are scheduled to be installed in four other European NATO countries.

What still remains unclear, however, is how far the Social Democrats are prepared to follow a campaign of civil disobedience that the peace movement vows it will carry out in the coming months to prevent the missiles from entering the country.

Environmental leader Joseph Leinen, speaking before more than 100,000 marchers in Dortmund, promised that the peace movement would soon escalate the anti-missile crusade to such an extent that the government would not dare to proceed with deployment.

Leading members of the Greens party, which holds 27 seats in the new parliament, plan to step up protests and say they are undaunted by the possibility of violent confrontations with the police.

Peace movement activists said they plan to gather May 9-14 in West Berlin with protest leaders from other European countries to plot a concerted campaign through the summer and fall that will culminate in mass demonstrations in NATO capitals Oct. 22.