One was the plagiarism by one of its MPs last year, when Mr Pritam Singh passed off an Internet article "word for word" as his own in a parliamentary speech.
The other was the award of a contract in 2011 - without any tender - to a company owned by close WP supporters.
During last year's Budget debate, Mr Singh called for an ombudsman but failed to attribute his speech to a blogger's post written in 2008.
He later said he had the blogger's permission to quote liberally from the post.
He reiterated this in a Facebook post last night, adding: "While my conscience has always been clear on the matter, I leave the public to judge why the PAP officially raised this issue some 16 months after it took place, that too in the context of a completely separate matter."
Mr Lee, in his statement on Friday, also pointed out that the WP-run Aljunied-Hougang-Punggol East Town Council (AHPETC) failed to explain why two years ago, it appointed a company owned and run by close party supporters to handle its affairs.
The People's Action Party (PAP) disclosed in May, during a parliamentary debate on town councils, that a tender was not called and the company, FM Solutions and Services (FMSS), had been appointed at a much higher price than the prevailing rate.
"Now FMSS, running AHPETC, has tried to charge hawkers extra for cleaning their hawker centres, and Ms Lim and Mr Singh have tried to cover it up," said Mr Lee.
Mr Singh, who is also the vice-chairman of AHPETC, which oversees the hawker centres involved in the cleaning row, insisted at the height of the controversy last month that no town council staff had asked hawkers to pay extra for cleaning the high areas.
These costs are borne by town councils.
This was WP chairman Sylvia Lim's position as well on Tuesday, after a dossier of notes and letters on the issue was produced by Environment and Water Resources Minister Vivian Balakrishnan.
He said it showed that Mr Tai Vie Shun, a property manager from the WP-run town council, had asked for it.
Dr Balakrishnan framed the issue as one about clean politics, rather than the cleaning of hawker centres.
This point was repeated by Mr Lee on Friday.
He went into detail on why integrity and honesty were important in politics, and why WP chief Low Thia Khiang's description of the charges made against his WP colleagues as "personal attacks" was wrong.
The country's success has been due to honest, upright politicians whom the citizenry can trust to "uphold the public interest, to speak the truth even when it is inconvenient, and to admit mistakes when things go wrong".
This, he said, is how the Government has built trust between Singaporeans and their leaders. If politicians cannot be trusted to tell the truth, then they also cannot be trusted to safeguard public funds or public interest.
He also said that before any minister accuses someone of dishonesty, "he must make sure that he is fully able to back up his charge".
On Wednesday, a day after the tense debate in Parliament, Mr Low said he disagreed with Dr Balakrishnan that the issue was about integrity and clean politics.
"It is market cleaning. Let's put it right and into proper perspective," Mr Low had said.
The WP's case is that the issue is a misunderstanding that arose from a "misleading" e-mail sent to the town council by the National Environment Agency on Feb 7, and from confusion over whether the discussions were about annual or quarterly cleaning. High areas do not have to be cleaned in the latter case.
Political watchers like former Nominated MP Zulkifli Baharudin said on Friday night that the Prime Minister has a point when he framed the issue as one of integrity.
The reason Mr Lee is wading into the debate, he added, had to be seen in the wider context of how opposition supporters, especially those online, are giving credence to statements made by non-PAP politicians without much regard as to whether they are truthful.
Said Mr Zulkifli: "After this episode, the lesson is: Politicians must get their facts right, especially if they want to use it for political advantage."
Get a copy of The Straits Times or go to straitstimes.com for more stories.