Construct a PDA for at least one $w_i$ $\neq$ $w_{i + 1}^r$?
Use nondeterminism to guess an index $i$ for which $w_i \neq w_{i+1}$. The machine reads its input until it nondeterministically chooses a $w_i$ and places it on the stack. Afterwards, it compares $w_{i+1}$ to the content on the stack symbol by symbol. If the comparison fails, the machine accepts.