I assume that the State rewards its managers. So, they have more money. For the colony- or station-bound managers it means that their lifestyle can be a bit more luxurious (but not too luxurious - after all, duty for the State and so on) and their children are likely better off than those children whose parents have smaller paychecks. Where the system breaks is when higher-level executives (and a lot of mid-level managers, too) can start to afford private education and, should they be so inclined, bribes to have their children in better positions. Even on the surface there might be relatively little corruption that can be measured (as in money or wealth changing hands) but a kind of network of favours in place. (I know a guy who knows a guy who...) You do look after your friends and you can trust they look after you.
As such, in most Caldari corporations, there is still very likely class separation due to managers having more personal wealth. In some corporations it might be different than wage - say, some people having access to a larger variety of goods - but in one way or another, the current executives are still in a better situation than their underlings. Apparently, in some corporations they had been able to establish a kind of a class system, where the children follow their parents. ("Mill town mentality") This is something that Heth worked to break. (With a rather hamfisted way, since there likely still those that were genuinely good at their jobs.) What we don't know is how many retained their pre-purge jobs and how many people were installed because they were Provist yes-men.
I cannot see the Caldari Navy being bossed around by Heth. Because if they bow down to one CEO, no matter how powerful, then SuVee and other corps could also expect to be able to use the Navy for their own ends. However, while there is documented nepotism in the Caldari Navy, I'd assume that the Navy - by the virtue of being one of the most esteemed institutions in the State - is able to get enough bright minds to keep the effects of nepotism relatively minor and mainly maintain meritocracy.
I can see several angles on the new regime. Naturally those who were backed by the "old money" and the network of formerly-high-level managers aren't going to be happy. Lots of feathers were ruffled for those who know what Heth did right was right, but it's wrong because they didn't get to do it. And then there are lots of possibilities to gain from the meritocracy by playing the game as intended. And even more by trying to fix the game, as the power vacuum created by fired and/or reassigned non-competent managers is being filled. Also, as the Caldari economy has been growing (due to increased consumption of the war machine), while this isn't a very sustainable path, fast growth always creates opportunities for those of enterprising, opportunistic mind and questionable morals.