By Douglas Winslow Cooper
“I observed him running” or “I observed his running”…which is correct?
First, he was running, and you were not. So we don’t need, “Running, I observed him.”
If you are emphasizing that you observed HIM, and he happened to be running, then the first is correct, and “running” is a participle [verb form used here as an adjective].
If you are emphasizing that you were more focused on the RUNNING than on him, then the second is correct, and “running” is a gerund [verb form ending in “ing” used as a noun], and you use the possessive case of the pronoun, “his.”
I often see mistakes in cases like these.