DETROIT—China has poured more than $40 billion into real estate across the world over the past seven years. But in a number of places, Chinese investors are running into snags peculiar to local markets.

In London, a Chinese developer’s £500 million ($768 million) proposal to rebuild the historical Crystal Palace in Crystal Palace Park crumbled after it missed a deadline for filing plans. In Australia, the government ordered a Chinese conglomerate to sell a $31 million house it recently bought, citing restrictions against foreign...