Here is an example from: http://threatpost.com/en_us/blogs/researcher-publishes-android-browser-exploit-110810
"Researcher MJ Keith published a Reverse Shell Exploit that affects mobile devices running Android's 2.0 and 2.1 operating system on November 5. The shell code takes advantage of a known vulnerability affecting WebKit, a common component of Web browsers, including the one bundled with Android, that is used to render Web page content and manage Web browsing sessions. The hole could be triggered by visiting a malicious Web site, according to a description of the hole published by Mitre."
This was posted on the Dailydave's newsgroup on 01/26/11:
You've probably already figured out that this bug is in Webkit. Our
research team is currently checking out what is and is not vulnerable.
The initial results are this: we've got an exploit in development for
Android. The iPhone should be vulnerable, we're still researching that.
Chrome is a bit early to call, we're still testing there. The sound bite
here is this: anything that depends on Webkit should be checked out.
Re-cap: Yes there are vulnerabilities that can affect only mobile solutions.