Seriously? Learn web development?
No one hires PhDs for web development skills. It is only useful if you want to be a pure software developer, not a quant or a data scientist. It might even be a negative when applying for some jobs.
Well they might not be hired to do just web development but I think learning about the web stack is incredibly useful because it helps you get your work out to people. This is important especially in a (early stage) start up where you might have to rapidly prototype solutions and you can't have your own pet designer to whip up visualizations for you. In fact, if you read the blogs of some of the data scientists at twitter/linkedin, its immediately clear that they have some know-how of the web stack in the way they are organizing and visualizing results. (Everyone likes pretty pictures)
Not saying you need to be a web developer to write a blog. All, I am saying is that the web provides a way to do interactive visualizations in a manner not provided by Matlab/R/matplotlib. For example, colleague at Mozilla did this: http://skedasis.com/d3/smoothers/
No one hires PhDs for web development skills, but knowing some basics certainly opens up some doors. I wouldn't want to hire a PhD who would couldn't build at least a demo himself.
Could you describe a circumstance where such skills would be a negative?
They would be a negative for some quantitative finance jobs. Not because they make you a bad quant. There is a perception among practitioners (who are mostly math/physics PhDs themselves) and headhunters that web development people do not know enough math to be a quant.
To quote one well-known headhunter:
'Good point, there seems to be a correlation between "web design" and only ever having done fluffy crap of no value in this line of work. Of course, correlation is not fact but as a headhunter it is hard to avoid that prejudice'