With android, and I think probably Mobile Safari, scrollbars aren’t shown on scrollable divs unless you attempt to scroll the div, at which point they temporarily appear to show you your current scroll position.
I don’t use mobile devices much, so to me this behaviour is not very user friendly - it’s not obvious that the div is scrollable, and the overflowing content just appears to be cut off. (I noticed this when checking a Google maps page and the content in an info bubble appeared to be cut off at the bottom).
Looking at some of the comments in this bug report, it appears there are some hacks that can be done to force display of scrollbars. But, if no scrollbars is the default for mobile browsers, then maybe it would be obvious to most users that they can scroll the div?
What do you think?