Heterogeneous mixtures are those mixtures where the individual substances can be visually observed and in which the properties of the mixture are not uniform throughout and vary from region to region. Examples are cereals in milk, sand in water, soil, etc.
Homogeneous mixtures, on the other hand, have uniform properties throughout and have no observable distinction between individual substances. Examples are salt in water, sugar in milk, etc.
Although there is no specific set of properties that can be used to classify a material as heterogeneous or homogeneous, the closest answer would be the physical properties. The individual components of a mixture can be separated out by physical means. For example, cereals can be separated from the milk by filtration. The same can be used for sand in water. The soil can be separated into different size clusters using sieves (another form of filtering). Thermal means can also be used, like evaporating the water to separate sand from water. Another property that can be used is the visual observation of the presence of different mixtures. Finally, we can take small samples from different regions of a mixture and measure their physical properties (melting point, density, etc.). If they are the same, then it is a homogeneous mixture; if they are different, it is a heterogeneous mixture.
However, some of these physical means can also be used to separate out individual components of a homogeneous mixture. It's just that it is easier to separate out the constituents of heterogeneous mixtures as compared to homogeneous mixtures.
Hope this helps.
There is just one property to find if a mixture is heterogeneous. That is SOLUBILITY. If the components are soluble in each other and you cannot distinguish the components, it is homogeneous. And if the components of a mixture are easily known even after mixing and there occurs no solubilty, the mixture is HETEROGENEOUS.