I don't have this issue, all slides display correctly in Presenter Display and Rehearse Play, below is a screen grab of Keynote presenter display:
I note you have a MacBook, from past experience with hundreds of MacBook computers they all have issues relating to video graphic output, so I would guess this is a hardware issue and is not resolvable.
What font and build effect are you using?
Im happy to test a three slide test file from you that has this issue present, if you show a dropbox web address or other way to send the file I will test it for you.
Thank you for a great response! I mostly use build in dissolves and Gill Sans.
Last night I figured out that the problem is build ins. If I just use regular transitions between slides everything works fine.
I still think build ins look better, but at least now I can add some kind of movement to my presentation.
Once again thank you for your reply!