Certain Linux distributions (specifically Ubuntu 10.10 and later, and possibly others) have placed restrictions on the ptrace(2) system call that cause jinfo, jmap, and jstack (and the Serviceability Agent) not to work. See 7050524. This is also documented in the JDK 7 release notes [1].
There is probably nothing that can be done in the tools themselves to fix or to work around this problem. Working around the problem requires a system administrator to change the system configuration.
The jinfo, jmap, and jstack man pages for Linux should have some information about this limitation. At the very least they should refer to the PTRACE_ATTACH section of the ptrace(2) man page [2]. Perhaps the man pages should also include information about the workaround. See the workaround section of 7050524 for specific details. (However, employing this workaround makes the system less secure, so it may be unwise to encourage people to do this.)
I'm not sure which distros this applies to. So far Ubuntu 10.10 and later are the only ones I've confirmed. The ptrace restriction facility has been checked into Fedora 17 but is disabled by default [3]. However, it may be enabled in the future, which will introduce the same issues as in Ubuntu.
There may be other areas of the system (such as the Serviceability Agent) that are impacted by the ptrace restrictions. We should consider updating the documentation for them as well.
[1] http://www.oracle.com/technetwork/java/javase/jdk7-relnotes-418459.html
[2] http://manpages.ubuntu.com/manpages/precise/man2/ptrace.2.html
[3] https://lists.fedoraproject.org/pipermail/devel/2012-April/165745.html