THE HOUSE HAS all but closed its 18-month investigation of allegations that South Korea, in the early 1970s, took out insurance against a post-Vietnam American withdrawal from Asia by bribing congressmen. A final demand is being made for the testimony of Kim Dong Jo, the stonewalling former ambassador accused of spreading money around Capitol Hill, but Leon Jaworski, the House's special prosecutor, evidently has no further leads to follow. Earlier he had indicated that Ambassador Kim's testimony might involve 10 or so congessmen. But the House ethics committee the other day charged only four legislators with breaches of rules, for accepting gifts from rice dealer Tongsun Park. It referred perjury cases against two former legislators to the Justice Department, and cleared all other recipients of Tongsun Park's favors, including Speaker Thomas P. O'Neill and Majority Whip John Brademas, of wrongdoing.

In brief, something of a cloud remains over the House: It could not get to the bottom of a scandal staining its good name. But that is not to say it was less than diligent in pursuit of its members' misconduct. A case can be made that, had the House cut off security aid, rather than just economic aid, Seoul might have produced Ambassador Kim. We find that case questionable: Ambassador Kim, to spare his president, might well have lied. But the House, respectful - as we are - of the American security interests in South Korea, did not want to take military aid hostage. That led South Korea brazen its way through. In fact, South Korea might have welcomed a cut in military aid: It would have brought Jimmy Carter's troop-withdrawal plans to an abrupt halt.

Republicans can be expected to compare the relatively slim results of the inquiry with the general sense that far from all Korea-related Democratic corruption has been exposed, let alone punished. The likely response, that the House could not push further without damaging American security interests, may be technically correct but will probably be politically unsatisfactory. That's fine. That answer is politically unsatisfactory.

The Korea scandal is part of a larger problem - money in politics - that has plagued American public life for years. Some reforms have been made to control special-interest contributions and get secret money out of politics, but not enough has been done. The speaker and the whip, while exonerated of improper conduct, had Korean connections that did not speak well of their judgment. They have all the more reason to redeem the integrity of the House by themselves leading the fight for further reform.