The stations are going to be broadcasting a mix of 4:3 and 16:9 content. I haven't messed with over-the-air lately, but it is possible some stations are pillarboxing 4:3 content prior to broadcast (meaning that they send everything out 16:9 and add bars on the sides - "pillarbox" - for 4:3 content). If this is the case and the converter box is correctly set up for a 4:3 TV, then you'll see those 4:3 programs in a frame of black (the studio-created pillarbox and the converter-created letterbox). If this is really what's happening, the only practical solution is a zoom feature on the converter that zooms in on that picture-framed 4:3 content enough to cut off all of the framing, at which point you'd need to toggle the zoom back and forth if you want to see the entire 16:9 frame when it's available. You mention this happening once with a commercial, but that may be because a lot of commercials are formatted as 4:3 with letterboxing (which looks rather stupid, frankly, when stuck onto an HD feed as 4:3). That leads us to the next possibility...

If you are getting TV shows with no bars above and below them but with bars to the sides in some cases (which I think is what's happening), my suspicion is that the converter box is configured for use with a 16:9 display. You will need to check on that and make sure it is set to a 4:3 display so that the converter box knows to letterbox 16:9 content and leave 4:3 content alone. I've only messed with one of these converter boxes (our secretary/office manager got one and brought it on for some help), but what I've seen hasn't impressed me much. If you can tell us what model your dad is using, we might be able to help.

Ideally, we should see two things: 4:3 content that fills the screen and 16:9 content that has black bars on the top and bottom, with a few odd commercials that have large black bars on the sides and small bars on the top and bottom (because the station is inserting a letterboxed 4:3 signal into a 16:9 HD broadcast). The reason for the jumping back and forth between these two standard conditions is simply because we have changed TV shapes and are in that transition phase. Because of the huge library of "catalog" content that exists in 4:3, we can expect to see pillarboxing linger forever.