Android phones can display unwanted and unsolicited websites, and I recently saw evidence of this.

Whilst this is possible with any brand of Internet-enabled phone (even one with filters and everything else), Android phones are especially vulnerable.  This is because the Android market is not vetted, and anyone could (theoretically) put anything at all into an app that you download.  This could well be a third-party advertising service (for example, Tefillah Times (free version) sends ads to your Android phone that appear in the notification area - these have included non-Jewish dating sites), or even malicious code.

In the instance that observed personally, someone's phone got stuck on an extremely hardcore pornography website, with no option to close it or navigate elsewhere.  I assisted to rectify this, and can confirm that it was not intentional in the slightest.

If you do have an Android phone, and want to avoid this, then be very careful which apps you download, and look carefully at the permission settings.  Some apps very closely resemble providers that you might be used to (e.g. Microsoft Hotmail) but are in fact developed by otherwise unknown developers.  Whilst not an issue in and of itself, there is a much higher degree of risk associated with these apps.

(My personal opinion) It only takes one hit of any hard drug to push someone down a slippery slope, and I can imagine that only one such image (and there were lots, they would not stop, and they were extreme) to damage an adult, let alone a child or teenager.  Please be very careful with mobile phones, especially those with unregulated apps, such as Android models.  Filters help, but they must be combined with understanding and knowledge, and some self-discipline.

PS I happen to be a close colleague with an professional Android developer, who agrees (emphatically) that anyone could place anything on the market.  Google responds reactively to problem-software, i.e. it might be around for weeks or months until enough people flag the app as an issue.