“Did he mention where he was going?”
You need to talk to your boss about urgent business. You call but his assistant answers the phone and says that he's been gone for most of the afternoon. You want to know where he is so that you can decide if you should call his mobile phone. If he's with a client, you'll leave a message with the assistant, but if he's out on some other business you'll call his mobile phone. You ask this to his assistant.
Did he mention where he was going?
This means to talk about something briefly. Even if a person says only a few words about a topic, that would be considered "mentioning" that topic. Other words like "say", "talk about", etc. sound like they require a longer period of discussion.
You can use "mention" with a simple noun:
Did she mention me in the article?
Or you can use a dependent clause:
You can also use the structure "mention (doing something)"
He mentioned going to the gym earlier in the day.