The logic test of the 74595 IC is indeed bad. I didn't have such an IC before, but now I have and checked this logic test on SN74HC595N from Texas Instruments.
At first I thought I might have bought a broken IC, but after careful analysis of the logic vector, I noticed that these wrong vector lines couldn't give the correct result.
Now I'll explain that.
The 74595 chip has 2 sections: the input, clocked by the SRCLK line, and the output, clocked by the RCLK.
Pin QH' should generally be in the same logic state as QH, but QH' is not controlled by /OE, so it can only take the values "L" and "H", while QH may still have the state "Z" (high impedance).
In line 21 of the logic vector QH' should have the value "H", because that was what it had in the previous line. Confirmed error!
On lines 2 through 16, the QH and QH' value is "L", but on line 17, QH' changes to "H" but not yet RCLK clock signal, so QH still has the previous value "L". Confirmed error!
On lines 18 and 19, QH' should already be "H". Confirmed error!
This is what the logic vector for the 74595 chip should look like.