I'm using beta Wikipedia, mobile version, on my smart phone.* Just now while editing the "Cover versions" section of "Blackbird (Beatles song)", I noticed that although the wikicode has "Template:Refimprove section" at the top of the section, the template does not appear on the wiki page. It only shows in the Preview and during the few moments of the "Saving..." display.
*Samsung Verizon Android Galaxy S-3, SCH-I535
OS v4.4.2
That's correct. This kind of infoboxes are hidden in mobile (because they aren't optimised for it). Actually, we parse the information and display it with the "This page has issues" Overlay link, but actually only for the Lead section (the first one) and for contents in the editor preview. I'm not sure, if we want to display it for other sections, too :/
We only show cleanup templates at the top of the page on mobile (and we collapse them into 'This page has issues' section. In mobile they are hidden in sub sections as they break the reading experience and we don't lift them up into the top of the page as they can be confusing. This is an editor feature which we do not plan to expose in the mobile web site.