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.