The best example is the shari'a police which for example has more rights than the usual police, as they might even be allowed to punish without presenting people to a court (needs to be checked).
This "officers" (called muttawi' مطوع are on the beat and for example check whether people have closed or left their offices and shops when prayer is held in a mosque after the adhan (I'll add some references later).
They had the power to arrest unrelated males and females caught socializing, anyone engaged in homosexual behavior or prostitution; to enforce Islamic dress-codes, and store closures during the prayer time. (Source wikipedia)
Of course their behavior has some kind of "Basis" in the sources of our religion. But one must ask himself if the Prophet() said I would do such and such, but didn'd do it, why shall we do it, are we more righteous than him?
In Iran you'll find a similar shi'a version. In many other Muslim countries such police departements more or less exist -not always independetly from the regular police departement-, but in most of them a punishement can only be applied after a juridical verdict by a court.
Also read in wikipedia.
There are also for layman less detectable claims: like changes of some well known books or ban on them. Like Ihya' 'ulum ad-Dyn of al-Ghazaly, some Kuwaiti scholar pretend that the chapters on sufism have been deleted or changed in the saudi-Version of majmo' al-fatawa (full collection of fatwa) of ibn Taymiyyah, tafsir al-Jalalayn has been replaced by commentaries of salafi scholars when the original commentators have used sufi interpretations. ... One would need to check if this is correct by buying books there and comparing them with copies printed elsewhere.
Scholars including al-Albani and his followers have written many papers showing that the grave of the Prophet () shouldn't be/stay in the mosque
and offered weird sollutions for that issue.
Less important might be the ban of Imams from the haram of Mecca because of their non-Salafi doctrine and the replacement with salafi scholars.