I am running 24x7 Scheduler ver 3.2.3. I am setting Job Notification for Job Start, Job Finish, Job Error, to send email to SMTP. When the job starts on the Master Scheduler, I get an email. But I don't get any emails form the Remote Agent server when the job errors or finishes. Why?

Job triggers (schedules) and job notification actions are always processed by the Master Scheduler. Remote Agents only execute the main job part. If you want to send emails from agents you need to add this functionality to the job itself.
In the event of remote job failure or finish event you should also get an email from your Master scheduler. If job logging option is enabled you should see in the Master scheduler log something like

Job XXX started.
Job XXX start notification message sent
Remote agent AAA contacted, job XXX submitted to agent AAA for execution
Job XXX finished
Job XXX finish notification message sent

: I am running 24x7 Scheduler ver 3.2.3. I am setting Job Notification for Job
: Start, Job Finish, Job Error, to send email to SMTP. When the job starts
: on the Master Scheduler, I get an email. But I don't get any emails form
: the Remote Agent server when the job errors or finishes. Why?

So you are telling me that these jobs have to run synchronously always, or the job Notification values will not work. This creates significant problems with job dependencies and concurrent processing on all remote agents, and indicates a HUGE problem. How do I make the jobs on remote agents run asynchronously if I have to submit them synchronously?
I have a true Enterprise environment, and am expecting thousands of jobs to be initiated from the master and run on Remote Agent servers mostly asynchronously.

: Job triggers (schedules) and job notification actions are always processed by
: the Master Scheduler. Remote Agents only execute the main job part. If you
: want to send emails from agents you need to add this functionality to the
: job itself.
: In the event of remote job failure or finish event you should also get an
: email from your Master scheduler. If job logging option is enabled you
: should see in the Master scheduler log something like

: Job XXX started.
: Job XXX start notification message sent
: Remote agent AAA contacted, job XXX submitted to agent AAA for execution
: Job XXX finished
: Job XXX finish notification message sent

No it wasn't said! Job run time mode wasn't even mentioned. What was said is that all notification actions and events are processed in one central place (on the master schedulers) exactly for the purpose of orchestrating different jobs running on different systems.

: So you are telling me that these jobs have to run synchronously always, or
: the job Notification values will not work. This creates significant
: problems with job dependencies and concurrent processing on all remote
: agents, and indicates a HUGE problem. How do I make the jobs on remote
: agents run asynchronously if I have to submit them synchronously?
: I have a true Enterprise environment, and am expecting thousands of jobs to
: be initiated from the master and run on Remote Agent servers mostly
: asynchronously.