All space habitats have serious problems that planets don't, but generation ships in particular have severe issues. The radiation shielding against cosmic rays would have to be huge, but beyond this there are two fundamental problems I see here: the first is absolutely fixed which is thermodynamics. The other conceivably could be corrected by AI or genetic engineering, and that is conflict between humans and social breakdown.

With thermodynamics, energy could be produced efficiently through nuclear fusion, but more concerning is material loss. Generation ships seem to be trying to be a closed system, but inherently will actually be exothermic. Anytime material is lost (e.g. leaking air) it's gone forever. This also means meaningful economic growth is impossible. If you want GDP per capita to go up you need to start at a high population and then experience population decline, which has been linked to social problems independent of wealth, over the centuries-long journey.

With human conflict and population dynamics, social breakdown is inevitable. Obviously, Biosphere 2 failed, but beyond this is the human crew itself. It's clear to me that the crew's values will evolve beyond the original goals of the sponsors, but that's assuming they even make it to the destination. The middle generations will lack motivation. Anthropologist Cameron M. Smith has calculated a minimum crew in the tens of thousands, because he assumes at least one population catastrophe in a 150-year voyage; learning of this paper really raised the issue to me that technological accidents happen and civil wars break out.

Potentially though, it could still work, but how hard do you guys think it would be?