<p>I'll address the issues that I think are at the heart of your concern separately.</p>

<p><strong>Provocative Titles and Visibility</strong></p>

<p>This section stems from @cardinal's comments above:
Part of the popularity of the questions you cite is due to the choice of title.  I think we all are quite susceptible to the power of first impressions, and thus can be swayed to 
read or skip an article/post/answer/book/etc based on its title.  Any medium that allows for a piece of work to conspicuously display a title opens the door to the use of sexy, attention-grabbing titles to garner views.  </p>

<p>On top of that, the particular questions acquired numerous views quickly, and thus was included in the Network side-bar of 'Hot Questions', increasing the questions visibility and thus, increasing the likelihood that people would 
click the link to the question, giving it more views (and possibly more votes).  And to somewhat belabour the point, but what information is displayed in the 'Hot Questions' sidebar?  The title of the question.</p>

<p><strong>Accessibility to non-experts</strong></p>

<p>Also mentioned by @cardinal is that the questions were quite accessible to people who wouldn't consider themselves as statistics- or data analysis-experts.  They include real-word concepts that people, regardless of background, are familiar with (Facebook, Amazon, interview questions), 
and the questions were posed in lay-person terms.  Concerning the Amazon question, I'd say the way in which the question is worded is not a problem, but rather a very good thing.  The "deep" questions you may be searching for do not
necessarily need to be asked in an esoteric fashion.  There are numerous questions from the Math.SE which concern deep, philosophical concepts, but are framed in such a way that not only does it not repel non-mathletes, but also reels them in.  A really great, recent example is <a href="https://math.stackexchange.com/questions/661855/is-it-faster-to-count-to-the-infinite-going-one-by-one-or-two-by-two">this</a>.</p>

<p>And when you combine accessibility to non-experts with a catchy title and place it in a prominent location, it'll be hard to stop the rise in view count.</p>

<p><strong>Depth, or lack-thereof</strong></p>

<p>I'll mainly focus on the Amazon question for the next couple sections.  The Amazon question is deeper than it first appears.  To quote @whuber's comment from the original question:</p>

<blockquote>
  <p>...the point of this question is not to obtain a mathematical answer
  but rather to see whether the interviewee thinks carefully about what
  assumptions need to be made in order to obtain a reasonable,
  defensible answer</p>
</blockquote>

<p>Being cognizant of and understanding the assumptions that are explicitly and, more importantly, inherently made when approaching a problem is an important and deep issue.  Quoting @whuber again, </p>

<blockquote>
  <p>Thus, we ought to consider any single, definite answer to this
  question to be incorrect--or at least not worthy of getting a job
  offer from Amazon. The answers that point out the ambiguities and
  discuss the assumptions are the ones that have merit.</p>
</blockquote>

<p>I think that if someone provided a clear, detailed answer addressing the issues @whuber brings up, worthy of many positive votes, then the question becomes one we can use as an example of a <em>fantastic</em> question on this site.  </p>

<p><strong>Is it a problem?</strong></p>

<p>First, are "soft" or "shallow" questions a problem?  I'd say not necessarily. There are numerous questions on the Math.SE which some can deem "soft" or "shallow" (and some have provocative titles), gained much popularity very quickly, but bred good discussions and sometimes really great, thoughtful answers (Exhibit <a href="https://math.stackexchange.com/questions/71874/can-i-use-my-powers-for-good">A</a>, <a href="https://math.stackexchange.com/questions/54431/why-do-people-use-it-is-easy-to-prove">B</a>). If the result is interesting discussion, I worry less about its genesis.</p>

<p>I think it's important to note here that SE has the Reversal badge, which is awarded to a user who provides an answer of +20 score to a question of -5 score.  We reward those who can provide an excellent answer to a terrible question, so why would we not also condone a great answer to a "shallow" question?</p>

<p>And specifically, are the questions you cite examples of a problem present in this particular SE, or the SE Network in general?  </p>

<p>I'd say no.  Concerning the Amazon question, from the answers and the discussion above it's apparent that the question is deeper than it seems at first glance. 
If I were to have a problem with it, it'd be that multiple answers arrive at the same conclusion using the same means, i.e. they're not adding anything that isn't already there.  So actually, your issue (and maybe my issue) with it may lie in the answers, not the question itself.</p>
