The WCLK by itself doesn't really tell you anything. You'd need to look at it alongside a data line and bit clock to see any issues with alignment, polarity, etc.
As for your MCLK problem, I doubt very seriously that it's a board issue. If it were, we'd never be able to get any audio examples to work, ever. And that isn't the case.
It's hard to tell what is going in Figures 4 and 5, because your pictures don't show the voltage or time per division; I can't tell how the voltage is changing or whether the clock frequency has changed. Anyway, figures 4 and 5 actually look like a probe grounding issue. I've seen people ground the probe at some connector's shielding rather than a GND test point and get behavior like that. If not, then you might have the AIC3106 and McASP driving the MCLK at the same time. This is a digital signal, so it has only two levels: low and high. If you have these intermediate levels, you more than likely have a measurement issue or a drive conflict.
Do you know for sure who is driving the I2S clocks? If not, this would be a good thing to check. If you're working with digital audio and you have almost any kind of audio issue, it's ALWAYS a good idea to look at your clocks and data (together) as a first debug step. Certainly it's a step that you have to take before concluding that you have bad hardware.
If you're running the same code on multiple boards, it's not surprising that you see this behavior on every board that you try.