-The use of dots in inorganic chemistry:
Let's take the example of copper sulfate penta-hydrate: $\ce{CuSO4. 5H2O}$. The dot here is used essentially as an expression of ignorance to indicate that, though the parts of the molecule separated by the dot are bonded to one another in some fashion, the exact structural details of that interaction are not fully expressed in the resulting formula.
Using Alfred Werner’s coordination theory that indicates that four of the five water molecules are actually bonded directly to the $\ce{Cu}$ in the form of a complex aquo ion $\ce{[Cu(H2O)4]^2+}$, then the formula is better expressed as $\ce{[Cu(H2O)4][SO4].H2O}$
So, the dot here signifies ignorance of how the subunits of a formula are structurally related.
-The use of dots in phase diagrams:
Let's take the example of the ternary phase diagram of $\ce{Na2O}$,$\ce{Al2O3}$,$\ce{SiO2}$. The formulas of
the various resulting complex sodium aluminosilicates
are all expressed in the form $\ce{a Na2O.b Al2O3.c SiO2}$
in which it is implicitly understood that these initial starting components do not exist as such within the resulting compounds. They represent the combining ratios of the binary/ternary starting materials required for the synthesis of the compound.
For more details, please see http://www.che.uc.edu/Jensen/W.%20B.%20Jensen/Reprints/134.%20Dots.pdf