An open society is not neutral to innovation. Innovation must be argued for, but existing structures continue even if no-one argues for them. An open society can only overcome this objection, if first there is a dissolution of all existing structures, a global 'restart'. Even then it does not follow, that there should be a single new society - the logical error of contractarian liberalism.
In an open society, innovation is exposed to the maximum possible opposition. Everyone can participate in opposition to innovation: there is no institutional structure, to protect innovation from this openness.
Open societies tend to singularity: if there are two open societies, they will logically open their borders, and ultimately fuse.
In an open society only one possible current state can exist: the outcome of the processes in the open society. No alternatives or plurality are possible. The supporters of an open society claim that process legitimises its outcome, but there is no logical basis for this claim.
An open society has a centering effect, an inherent defect of all liberal societies. Ideas are exposed to pressure, and the most extreme ideas are exposed to the most pressure: they tend to disappear over time. The extremism is judged by pre-existing norms: an open society on a Christian base will become more Christian. In other words, there is not only centering, but it centres on existing tradition and values, and not on innovation.
An open society is inherently repressive toward enemies of the open society. The views of right-wing liberals indicate, that in a perfect open society most political activity would be forbidden as subversive. The Latin American military dictatorships of the 1970's were a classic example of the belief that extreme repression is necessary, to 'guarantee freedom'.
An open society destroys moral autonomy. The current state of an open society, at any given time, is the result of complex processes involving every member. In a perfect open society, individual action can never produce individual results: the results may even be contrary to the intentions. In either case, moral action is impossible. In existing liberal societies there is often explicit opposition to moral attitudes. Employers demand that employees are 'flexible', loyal to the employer, and 'customer-friendly' rather than ethical. In this way, the preferences of employer and customer are substituted for the moral judgment of the employee. In turn the employer as entrepreneur is 'market-oriented' rather than ethical.
The open society recognises no objection of conscience - and as the items above show, there are good reasons for conscientious objections.
There is no procedure to leave the open society. This is also an inherent defect of contractarian 'hypothetical assembly' models such as that of John Rawls, or more explicitly Bruce Ackerman.
Because of the lack of neutrality, the centering effects, and the inclusivity, an open society tends to act as a filter against innovation. Openness does not simply cause innovation: the case of high-speed rail transport in the US is a good example. Here, despite the stereotype, the advanced technology is European, and the technological conservatives are US-Americans. European manufacturers of high speed trains are free to sell them in the US, and the US itself is an open society. Innovation did not follow, as advocates of the open society would claim. None of the proposed projects has got started, most have met opposition: Americans prefer to stay in their cars. Innovation is not a contagious virus.
An open society certainly tends to reject innovations which do not intensify or extend the open society itself. The perfect (hypothetical) example is the construction of a second Internet, fully segregated and incompatible with existing network technology. Although a new and separate Internet is an innovation, it contradicts the principle of interactive openness, and an open society could not tolerate it.
Liberal democratic open societies create hierarchy, and amplify it. The cause is a combination of a competitive labour market with a selective educational system. Put simply: the richer the parents, the better the educational achievement of their children, and the better the education, the higher the income in the following generation. Of course there are exceptions, but unless the exceptions form the majority, this 'malsystem' will amplify structural inequalities in each succeeding generation. This is probably the best-researched social effect of liberal societies: there is overwhelming evidence that they limit social mobility. So far as I know no research in Western Europe, has ever shown above-average educational achievements, for those with below-average incomes or status. Yet that is by definition necessary, to allow social mobility through education.
Due to this combination of inequality, hierarchy and centering effects, liberal-democratic open societies are dominated by stable elites. These elites often correspond to the pre-existing high-status groups, in terms of gender, age, ethnic group, language and class. In European nation states, economy, law, parliament and government are dominated by middle-class and upper-class male members of the dominant ethnic-linguistic group. Where there are religious and cultural divides, this elite is predominantly from the dominant religious and/or cultural group. Like all stable elites, these national elites are arrogant and oppressive.