I scanned through the change logs for autofs and saw nothing to indicate that the 'dump maps' / automount -m command was or will be deprecated, so it should pretty much universally work.
It does require root to run; possibly that was an issue? If it is absolutely not working on a particular PC, please provide the version (automount -V) and the OS Type and full version.
You can get the same information - the list of all possible mounts - the way that you said you didn't want to: cat /etc/auto.master That will provide a rolled up list of monitored spots. To get just the mountpoints (no comments or extraneous info) use grep -vE "^[+#]" /etc/auto.master To make this painless, set an alias (bash syntax) alias autoMaps='grep -vE "^[+#]" /etc/auto.master and you'll save yourself the hassled of parsing the output (it strips out everything but the mounts).
This approach would be reasonable (in my opinion) for a straightforward autofs configuration. A complex system with LDAP, multiple master mount points and dozens of other configuration possibilities would make it far less serviceable.
df -a -t autofs or mount -t autofs will show you mounted autofs points.
The issue with the /etc/init.d/autofs status command is due to the now widespread use of systemd instead of init style (e.g. SysV) for initialization / PID 1 / user space bringup.
On systemd systems there is an equivalent command:
systemctl status proc-sys-fs-binfmt_misc.automount which provides output in this format
● proc-sys-fs-binfmt_misc.automount - Arbitrary Executable File Formats File System Automount Point Loaded: loaded (/usr/lib/systemd/system/proc-sys-fs-binfmt_misc.automount; static; vendor preset: disabled) Active: active (running) since Fri 2016-06-10 05:01:07 EDT; 2h 42min ago Where: /proc/sys/fs/binfmt_misc Docs: https://www.kernel.org/doc/Documentation/binfmt_misc.txt http://www.freedesktop.org/wiki/Software/systemd/APIFileSystems That command doesn't exactly jump off the finger tips, but if it something you would run frequently you could setup an alias for it. In bash shell, alias autofsStat='systemctl status proc-sys-fs-binfmt_misc.automount
I think everything you are looking for is there, but has changed slightly. If you have situations / PCs where it definitely doesn't work, please update the question with the specific environment and I can help dig into it. It could be bug, really old version (or both), or potentially a configuration issue.
If I missed the target on this answer, just let me know more specifics about your problems.