Molecule where an sp3 chalcogen is connected to an sp2 atom
Out of the blue, consider triphenyloxonium cation. It is non-planar thanks to bulkiness of the phenyl groups.

Another possible example is mono-epoxide of allene. Considering oxygen atom as $sp^2$ here is unconvincing since it would involve huge angular strain, much higher than for a structure with $sp^3$ oxygen.