Check dimensions, page order and numbering if applicable. Where elements cross two different pages, unless a centre spread they will no longer be side-by-side as they are imposed for printing - ensure that these items will align properly when they meet again at finishing. Check colours to make sure they appear as you intended. Where marking a proof for correction use a suitable permanent fine pen if possible, a different colour to the text preferably to ensure your amendments stand out. There are commonly used editor's marks which can be used if you are familiar with them, otherwise stick to clear and concise marking. A good way to mark an alteration is to circle it or draw a single line through it and then put a cross in the margin alongside with a comment/correction note. Where you require an element to move, give an exact measurement, this will ensure that there is no confusion and the result is as you expected.
A mocked-up dummy is also supplied to ensure the correct pagination.