One common way is:
die() {
    IFS=' ' # make sure "$*" is joined with spaces
    # output the arguments if any on stderr:
    [ "$#" -eq 0 ] || printf '%s\n' "$*" 1>&2
    exit 1
}
then you use it like this:
mkdir -p some/path || die "mkdir failed with status $?"
Or if you want it to include the exit status, you could change it to:
die() {
    last_exit_status=$?
    IFS=' '
    printf '%s\n' "FATAL ERROR: $* (status $last_exit_status)" 1>&2
    exit 1
}
and then using it is a bit easier:
mkdir -p some/path || die "mkdir failed"
When it fails, mkdir will likely already have issued an error message, so that second one may be seen as redundant, and you could just do:
mkdir -p some/path || exit   # with the same (failing) exit status as mkdir's
mkdir -p some/path || exit 1 # with exit status 1 always
(or use the first variant of die above without argument)
Just in case you haven't seen command1 || command2 before, it runs command1, and if command1 fails, it runs command2.
So you can read it like "make the directory or die".
Your example would look like:
mkdir -p some/path || die "mkdir failed"
cd some/path || die "cd failed"
some_command || die "some_command failed"
Or you can align the dies further on the right so that the main code is more obvious.
mkdir -p some/path         || die "mkdir failed"
cd some/path               || die "cd failed"
some_command               || die "some_command failed"
Or on the following line when the command lines are long:
mkdir -p some/path ||
  die "mkdir failed"
cd some/path ||
  die "cd failed"
some_command ||
  die "some_command failed"
Also, if you are going to use the name some/path multiple times, store it in a variable so you don't have to keep typing it, and can easily change it if you need to. And when passing variable arguments to commands, make sure to use the -- option delimiter so that the argument is not taken as an option if it starts with -.
dir=some/path
mkdir -p -- "$dir"         || die "Cannot make $dir"
cd -P -- "$dir"            || die "Cannot cd to $dir"
some_command               || die "Cannot run some_command"