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It seems to me that a good solution [for those worrying about lost content] would be to load the additional content once the user scrolls down to it, seeing as in this specific example (and in most mobile designs) the floats just end up beneath the main content. Having said this, as a user I really hate seeing my page lengthen just when the end is in sight; a button may be a less violent approach.
On a less logistical note, the question is ‘who needs to see this aside’ (1) vs. ‘who wants to see this aside’ (2). The first may be possible to deduce from the content of your website, but I’m not sure (2) can be (as I assume has been done here) implied from the device: I cry every time youtube gives me only super-LQ videos when I browse it with a Nokia.