connecting primary cells in parallel
Connecting cells in parallel will cause current to flow between/around/through the cells.  This is bad because it wastes the power (reduces the life) of the higher voltage cell, and, for non-rechargeable primary cells, makes the low voltage cell more likely to leak (fail, burst), and voids any warranty the cell manufacturer provides.

Putting a diode in series with each string reduces the available voltage, and wastes power, but it is better than allowing reverse current through a non-rechargeable cell.