1. Go to the page where the logo does not change. Click to Edit > Page Options (at the bottom of the page) http://i.imgur.com/EwMj68X.png
2. Make sure there is no logo assigned there http://i.imgur.com/tGXlQVc.png, because this value overrides the theme options
If these steps did not resolve the problem, then
Go to Apperance > Theme Options > Header, and make sure you have the right logo there. If you want to display a light logo -- which is for darker sliders -- then please make sure the light logo is assigned.
If these steps still did not resolve the issue, it's because you have imported the sample data and it broke the fields. So please kindly add a new page and copy paste your content from the other page. It will work.