How is the latest test result determined? What parameters / conditions are really used?

You may want to see the comment 12 in Workitem:
https://jazz.net/jazz02/web/projects/Rational%20Quality%20Manager#action=com.ibm.team.workitem.viewWorkItem&id=101947

Basically each testcase can have different TCERs, if TCER has different combination of environment + iteration, then they are considered as different groups. Each group(TCER) will have latest result(execution end time stamp) override
its own previous group. In Test Case view, if you see the last result icon of each test case: the result with the highest severity across all these groups of results would take precedence. The order of severity is(high to low)
• Blocked
• Error
• Failed
• Deferred
• Partially Blocked
• Inconclusive
• Incomplete
• Permanently Failed
• Passed
• Not Run
• In Progress
• Paused


From above, you can see the icon shows last result is Failed, but after failed, there are two other groups execution results: inconclusive and Passed in my test, since Failed has higher severity in the 3 groups, the icon will show Failed even though it is not the latest execution result for the Test Case.

If my answer helps you, please consider accepting it. Thanks

Appreciate the response, but I'm seeing that Passed is taking a higher priority than Inconclusive in my case below.  The Environment and Iteration are all the same. Your response indicates that inclusive is higher in the selection order.  So the latest TCER should be inclusive, but instead it's Passed.

 
Viewing the Test Results with some more details

I rarely use the GUI, only involved in the back end processing of results through REST.  Still trying to figure out why 814403 is marked as current (latest), my assumption would have been 812080.