I believe an aspect of emergency mode is that the root filesystem is mounted read-only, which is a complication...keep reading.
Connecting a keyboard to the device and running suggested command is an option, but outside of this question.
Yes. Jessie uses systemd which includes a new-fangled logger, journald. I think systemd is great, but since journald keeps its log in a binary format, it is a PITA for stuff like this (where you want/need to look for errors in the log without the system running).
There is a way to examine journald files using a journald tool on another system (see Wilf's comment below). Raspbian by default keeps the journald log on disk, but I've always disabled this since it tends to become ginormous (i.e., the binary format is not a space saving one).
This does indicate an advantage to journald, namely it keeps a system log in memory and hence does not require a read-write filesystem be available (making it particularly useful if you are running in emergency mode).
Fortunately, logging to disk can also be done in a human readable format via old school syslog, and Raspbian is default configured that way. The configuration (see
/etc/rsyslog.conf) dumps a copy of everything to
/var/log/syslog. This includes stuff from the kernel that you can view with
dmesg when the system is running.
There is a caveat: If the system failed before the root filesystem was mounted read-write, there will be nothing to read about whatever happened and no indication in the on disk logs that the system even booted.