Kinda hard to answer without clarity on what you mean by allegations. All allegations tend to work by exaggerating truth or distorting it, such as organ harvesting the Falun Gong coming from real state crackdowns on the Falun Gong as a far-right cult, but no actual organ harvesting.

If we just mean real missteps, I'm not a fan of how the PRC sided with Cambodia over Vietnam during the Sino-Soviet split. The cultural revolution also had excess that was avoidable, and the four pests campaign made legitimate famine worse.

For the modern day, LGBTQIA+ rights are lacking, but this varies heavily by region, and this has been getting better over time. There's also rural/urban development gaps, though the CPC is trying to address this as well. Most real issues are being worked on and are iteratively improving.