Why this happens
The reason to why this happens is because you have different design pages on your blog, but only apply your new design changes to the start page. When you do this, you will see your "old design" when you link a blogpost on e.g. Facebook and come to a page for a single post and not the blog's start page. If you've chosen to have sepratate design pages for your blog (start, posts & pages) you need to go in and change all of those design pages when you make new additions in your design to make all pages of your blog have the same look.
How to solve it
To solve the problem we recommend you to go to Layout in your blog's design and remove the separate design pages for Posts & Pages - that way all the pages in your blog will get the same look as the start page in your blog. If you still want to create separate design pages for Posts & Pages you can simply open new ones - and the design from the start page will be copied to your pages. After that you're free to contignue to work on your different pages.
Under You blog / Design / Layout you can see the different design pages you have. Above is an example of an account that has a separate design for Start and Posts, but not for Pages.