I found examples on StackOverflow for how to do curved corners on a UIImageView, and this worked fine when I was setting the image in my Xcode gui builder tool. When I then added some code to change the image at runtime, the curved corners were only partially working.
Here is the code I am using to try and achieve curved corners:
thumbnail.image = [UIImage imageNamed:self.video.thumbnailFileName];
thumbnail.contentMode = UIViewContentModeScaleAspectFill;
thumbnail.clipsToBounds = YES;
// round the corners:
thumbnail.layer.cornerRadius = 10.0;
thumbnail.layer.masksToBounds = YES;
// add a border:
thumbnail.layer.borderColor = [UIColor lightGrayColor].CGColor;
thumbnail.layer.borderWidth = 3.0;
BEFORE: When setting the image via the gui builder in Xcode:

AFTER: Setting the UIImage programmatically. Notice the curved corners look terrible:

The original PNG image being used in the app:

The issue here was a series of strange coincidences…
First issue was I had two versions of this image at one point, and somehow the first version I had was still being transferred over to my app bundle (or was in my app bundle from previous debug builds). That first one was a different since and wasn’t lining up correctly with the curved corners. So once I cleaned my build, that original file was gone.
Second issue was the second file had a slightly different filename, which I didn’t notice, and so that was the second reason I couldn’t get this working properly.
So … the code was right, just had issues with my image files! Sorry for the confusion.