With vertical hierarchy you face problems of orders and queries slipping through the cracks if your organizational tree and who's responsibility is who's isn't firmly set. On the plus side if you do have those firmly set then everyone is clearly aware of who they should report to or who they should go to if they have a question that another department/level of management must answer.
As for vertical communication it has the same problem: information slipping through the cracks as it is passed down or up through the ranks. The communication must be detailed in its objective and what information it's trying to convey/receive. The pluses are mostly obvious ones, like higher-ups always being aware of what's going on underneath them, and maybe more importantly lower-level workers knowing what their bosses want.
Vertical hierarchy has advantages in the sense that information flows systematically through all the ranks and file in an organization and hardly anyone can be left out, even for those who are absent from duty. On the other hand, its biggest disadvantage is that it tends to be slow and where vital information is needed on short notice, the organization is bound to suffer.