I got two questions:
1) What's the point on clicking the option to make a contest or a problem 'favourite' if you can't see a list of favorites problems/contests?
2) Why do it says 'favourite' instead of 'favorite'? Is it an error or is it something else?
Just wondering :P
2) It is something else: something like meter and metre, neighbor and neighbour. The first one, in your case it is the second one, is the American english.
If you have at least one favourite contest, you will be able to see "fav. contests" tab on your favourite page. If you have at least one favourite anything, you will see a "Favourites" link in the list under your rating on the left.
"favourite" is an english version of the word. "favorite" is an american version of the same word.
https://mirror.codeforces.com/favourite/contests
https://mirror.codeforces.com/favourite/problems
https://mirror.codeforces.com/favourite/blogEntries
https://mirror.codeforces.com/favourite/comments