Jonny,
I have no idea why BlueGriffon gives the strange effects that you have noted but rather than try to find an explanation what I suspect you want is a fix.
Your ‘buttons’ are just a list of links to somewhere. Each should consist of an image and a hyperlink. In some cases you have an image without a link in other cases you have a link but no image to click.
What is unconventional and technically incorrect, is that you have strung all the images together in a paragraph. Since they are actually a list of images and links they should be formatted as a list. This also makes fault diagnosis much easier.
To do this simply start an unordered (ul) list and insert list items with one image in each. You can then link the images as necessary.
You then need to set up the css needed so that the ul is
given list-style-type: none; (in the lists section of the style properties panel).
Each image will now start a new line. To avoid that for the li set display:
inline; (in the Position and layout section).
If you do that I think you will find your pages respond as expected. At least I hope so!