His remarks came as another former candidate for the Falkirk nomination, Gregor Poynton, admitted he had paid for 11 members to join the constituency party with a single cheque of £137 last July.
Mr Poynton, a former Labour election strategy manager and party organiser, said he had done nothing wrong. He told a newspaper: “I believe that I have at all times acted within the rules.”
Mr Clegg said that events in Falkirk were an “absolute mystery”.
The Liberal Democrat leader also said those at the top of Labour appeared to be “puppets on a string” for the trade union bosses who provide the bulk of the party’s funding, and described the controversy over the choice of a successor to MP Eric Joyce – who quit the party after a Commons bar brawl – as a “Monty Python parody of the Soviet Union”.
Earlier this week, Labour leader Ed Miliband rejected calls to reopen the party’s inquiry into allegations of vote-rigging in the selection for a candidate for the Falkirk West constituency.
Mr Miliband declined to look at the investigation again, despite the publication of e-mails from constituency chairman Stephen Deans which raised fresh questions about alleged attempts to sign up members who would support a candidate backed by the Unite union and alleged attempts to thwart the subsequent party probe.
Unite official Mr Deans and the union’s favoured candidate, Karie Murphy, were reinstated in September after a Labour investigation found no evidence of wrong-doing. Unite was cleared of the allegations after the key claim that people had been signed up to party membership, without their knowledge, was withdrawn.
However, party members who made the original complaints have since denied changing their accounts and Mr Deans has quit as Falkirk chair.
The row was also at the centre of the Grangemouth dispute, which almost led to the closure of the site’s petrochemical plant.
Mr Poynton’s admission was accompanied by anonymous claims by two new Labour members that their membership was paid for by him or his family in the expectation that the new memebers would lend him their support in the selection battle.
Mr Clegg said: “It’s like some sort of Monty Python parody of the Soviet Union. The whole thing is so mysterious, that the Labour Party is run like this.
“The Labour Party leadership appear to be puppets on a string run by these trade union bosses.
“How the trade union bosses then get elected, how they raise money, how they disburse money, is a complete and utter mystery to me.
“Something seriously dodgy clearly happened in Falkirk. It really is time the Labour Party leadership come clean with people about what happened so people know – given that this is a party that wants to run the country from May 2015 onwards – what kind of party it is.”
Michael Matheson, SNP MSP for Falkirk West, said the Scottish Labour leader Johann Lamont should step in to clear up the party’s selection procedures.
Mr Matheson said: “As if things weren’t bad enough for Labour, we now have reports that a senior party figure paid for new memberships in return for votes. Labour clearly has little regard for democratic procedures.
“The people of Falkirk deserve so much better than this, which is why I’m calling on Johann Lamont to clear up her party’s mess once and for all.
“This is a damning revelation and means Ms Lamont can no longer get away with saying nothing of substance on the issue.
“Despite the fact she is supposed to be leader of the whole Labour Party in Scotland, Ms Lamont just stands by and watches her party stumble to new lows in Falkirk without doing anything – she can no longer leave this matter to her party bosses in London.”
MORE ON FALKIRK