Recording does not show presentation filling up all the screen space

I always share an entire screen rather than an individual application.  If I present a wide-format PowerPoint show on my old-fashioned 4x3-ratio monitor, there are black bars above and below.  At the office, where I cannot work right now, I have a wider monitor that fits the PowerPoint better.  When I present a webinar from that computer/monitor combination, there is no black border around the video image.

You might try sharing an application, like PowerPoint, rather than an entire screen.  It might be better or worse.  You could set up a test GoToWebinar and look at the result logged in to another computer.

You can crop out the black bars with most video editor/converter tools.  I use Apple Compressor, which allows me to drag lines to where I want to crop the image. Then the resulting video does not have the black areas outside of the program material.