Is there a way to trim videos in a Slideshow?

You need to do the trimming from the Photos, All Photos or an album window while playing the video. The slideshow will include the trimmed version.

when you play the video, click the actions icon (the little gear). Click "Trim".

Then drag the yellow Trim handles in the film strip to trim the clip.

This is helpful to trim from either end of the video, but how do I cut out a section in the middle of the clip?

For that type of movie/video editing you'll need to use iMovie. Quicktime Player 7 with Quicktime Pro or other movie editor of your choice.