Sleaze, cronyism, conflict of interest, ministerial double-dealing; such are the common afflictions of long serving governments. Perhaps the remarkable thing, looking at the SNP's eight years in office, is that they haven't experience a serious sleaze problem before. Some think they now have one in spades.

The suspension from the party of Business Affairs spokeswoman and SNP MP for Edinburgh West, Michelle Thomson, after revelations about her property dealing, is highly toxic. The involvement of one of Alex Salmond's former special advisers, Jennifer Dempsey, in a deal to hand £150,000 of public money to the well-heeled organisers of T in the Park may be a storm in a teacup, if you'll excuse the pun. But it looks iffy to say the least.

These are not cases of corruption. No wrong-doing has been established and Ms Thomson is not even under police investigation; only her legal associates. But in politics, formal innocence is rarely enough.

After the creation of the Scottish Parliament it took only two years for Labour to be embroiled in the “lobbygate” affair – a kind of Caledonian cash for access scandal – after which the-then minister, Jack McConnell was fully exonerated. The Labour First Minister, Henry McLeish, wasn't so lucky. He resigned in 2001 over allegations that he sublet his constituency offices in breach of parliamentary rules.

Actually, he had been cleared by the Westminster Fees Office over the offence, but he ended up resigning nevertheless over “a muddle not a fiddle”. The ethical standards expected of Scottish politicians is exceptionally high; perhaps too high. The late leader of the Scottish Conservatives, David McLetchie, resigned in 2005 over a handful of unauthorised taxi chits.

But the public is rightly suspicious, following genuine "payola" scandals at Westminster in the 1990s. More recently, expenses scams revealing how MPs were financing duck houses and moat cleaning on the public purse damaged the reputation of politics in general.

So, the SNP is just going to have to take it. They've benefitted in the past from Tory sleaze and allegations of Labour cronyism. Now the boot is on the other foot. Opposition MSPs have every right to kick up a fuss about why a close ally of Mr Salmond was involved in an arrangement that handed a large sum of public money to a private company that was not in obvious financial difficulties.

The Culture Secretary, Fiona Hyslop insists that, in granting £150,000 to DF Concerts, she was protecting a landmark cultural event, T in the Park, of great economic benefit to the Scottish economy. But the events company had been making multimillion pound profits year on year, and its main sponsor, Tennents, isn't short of a bob or two.

Similarly, it may be the case that the police investigation into the legal practices of Ms Thompson's associates yields nothing, and that she is anyway in the clear. But the fact that her company was involved in flipping homes bought from distressed elderly homeowners – yielding large sums in “cash back” as the properties were rapidly remortgaged at much higher valuations – looks like sharp practice. This may be just how the property business works but it jars with the SNP's left wing, progressive politics image.

Eyebrows were also raised recently when Mr Salmond's former communications director, Kevin Pringle, joined Charlotte St Partners, a public relations firm that advises private clients on relations with government. Mr Pringle was regarded as one of the straightest spin-doctors in the business, and not even the most tribal Labour politician has accused him of sleaze. But such cross-overs into the private lobbying world are worrying.

People will naturally ask whether ex-spin-doctors do not enjoy privileged access to senior politicians. Certainly, that's often the first thing that the private clients ask about.

Relations with business are always dangerous territory for government ministers. In the effort to secure jobs and investment, they're often tempted to tell industrialists what they want to hear. This brings us on to fracking, the extraction of fossil fuels by blasting underground rock formations with toxic chemicals.

The Scottish Government has imposed an indefinite moratorium on fracking. But the boss of the petrochemical giant Ineos, Jim Ratcliffe, recently claimed that he'd been told by ministers that the Scottish Government was not against unconventional hydrocarbon extraction and that a green light on fracking could be imminent. This has infuriated environmentalists who believed that the Scottish Government was on their side.

Another accident waiting to happen could be over the Government's Higher Education Bill. This apparently innocuous legislation has generated widespread confusion, acrimony and claims of government interference. The Education Secretary, Angela Constance, has insisted that she only wants to improve democratic accountability in Scotland's 17 universities.

But campaigners who oppose the bill say they've been told privately that elected rectors, who chair the court in ancient Scottish universities, will simply become “ornaments” shorn of powers. The darker suggestion is that a manipulative government is seeking to impose centralised control and curb academic freedom.

This row is possibly a consequence of ministerial inexperience and there is no hint of corruption. But the claims of government double-dealing have added to the drumbeat of negative comment about the integrity of the Scottish Government. Too often, it appears to be saying one thing and doing another.

Of course, all long-standing governments find themselves attracting negative stories like these; they stick like barnacles to the ship of state. It will be the manner of Nicola Sturgeon's response that will determine whether and by how much the government's progress is impeded.

So, far, the First Minister has proved to be pretty tough on sleaze and on the causes of sleaze. She has not engaged in any knee-jerk defence of one of her most high-profile female MPs. Ms Thompson has been relieved of the party whip and no longer sits as an SNP MP at Westminster.

That is a humiliating demotion for the former managing director of Business for Scotland, and one of the most high profile figures in the referendum campaign. She claims that she is guiltless and is not even “helping police with their inquiries”. In accepting her resignation Ms Sturgeon is making a statement that conduct unbecoming will not be tolerated.

But what must keep her awake at night is the knowledge that there are 56 new MPs at Westminster, many with business backgrounds, who are largely unknown. There are also 80,000 new SNP members working their way through the organs of the party, some of whom may also have exotic connections or unprepossessing character traits.

But, hey: that's democracy. You have to work with what you get. And thus far the SNP's scandal control, in the face of a hostile press, has been pretty effective. Now they are facing their toughest test yet.