It might relate to CSS skew() function.
I used skew(+20deg) to a outside box and skew(-20deg) to a inside box, in order to make a Parallelogram box and keep the inside content normal.

Tested the same on mac 10.11.5 chrome version 52.0.2743.82 and canary - No blur text in sub menu

But i am able to see the blur text on win 8.1 chrome version. This can be seen from initial builds M30 as well - Please refer the screenshot

Firefox behaviour : Please find the screenshot

Chrome version tested was : 52.0.2743.82 and canary 54.0.2805.0

Issue observed on Linux as well

It is indeed due to the skew function. Removing it makes the rendering almost identical to FF. Not sure why but I'm guessing we're loosing precision due to rounding. Over to compositing team for further triage.

The problem is the combination of skew and layer promotion. If we haven't promoted the text and it's counter-skewed then it draws nicely (with subpixel AA) however the skew is applied after rasterization so if the text is drawn into a skewed layer it looks really blurry. There's an easy workaround if we composite the text into a separate layer after applying the counter-skew. See http://jsbin.com/gitige/edit?html,css,output

Perhaps we should consider skew within a promoted skewed layer for automatic promotion?

UPDATE:

In other pages such as: 
About Page http://bgoilfieldservices.com/about-us/
Services Page http://bgoilfieldservices.com/services/ 
The sub menu text looks normal.
Also, I tried delete content in the <section id="main">, the sub-menu text looks normal again.

Can we drive this to a plan of action? Any thoughts on flackr's suggestion?

vollick agrees with my suggestion to automatically promote skewed elements within a promoted skewed element to improve the output quality. Chris, does this sound good to you?

I can take the bug.

Hi Tien-Ren, could you please take a look at this bug? Chris said you might "have a possible SPv2 solution could be to raster
everything in screen space." 

BTW, the fix based on Rob's idea above: https://codereview.chromium.org/2714283002/.

I think Rob's idea is definitely worth trying!

Yes, being able to raster everything in screen space is a surprising byproduct of recent layerization algorithm improvement. However I feel there are still a lot of unknowns in there (e.g. performance? LCD text? how bad the edge bleeding?), and I don't think it will be a shipping goal of SPv2. It is more like an experiment that previously couldn't be done, but become open once SPv2 is ready.

Leave the bug as-is till SPv2 is ready.

Remove myself from owner as there is no plan to act ATM.