Yes, there are exceptions in physixcal properties of metals and non-metals.
These are as follows:
1) Mercury and gallium both are metals but at room temperature, they are in liquid state.
2) Metals have high melting point. But mercury is low melting metal.
3) Metals generally sink in water due to high density. Exceptions are lithium, sodium and potassium. The density of these elements is lower than that of water and hence they do not sink.
4) Most of the non-metals have very low density. Exception is diamond, a form of carbon. Diamond is one of the strongest known substances.