The only two properties that report on the results of the last execution of a task are LastRunTime and LastTaskResult. LastRunTime gives the time when the execution started and LastRunResult gives the exit code for the executable specified in the task's ExecAction that fired.
For a bunch more detail, you can create a TaskEventLog object for the task and iterate through the events fired by the task. However, depending on how your task reports its result, this may not give an answer either.
For a bunch more detail, you can create a TaskEventLog object for the task and iterate through the events fired by the task. However, depending on how your task reports its result, this may not give an answer either.