I am trying to get 'Battle of Whiterun' done.
When I finish it and the battle is over it says 'talk to the Jarl of Whiterun', so I go and talk to him, then I get...

"Quest Completed: The Battle of Whiterun"
"Quest Started: [...]"

The quest in my Journal tells me to talk to Tullius, but no marker is shown for this. If I go and find him the quest continues but again it is called [...] and there are no markers. This next part is more complicated because the objective is to 'regain the pale'. I dont actually know where the Imperial camp is in this area, anyway, I digress.

Anyone else have these problems?

This is a known problem that happens when you patch on an existing save. Some of the Radiant aliases seem to drop off, whereas on a new game they are fine. Usually seen with notes where [...] goes where the text should be.

However it can also be caused by mods so I would suggest to disable and even move them all somewhere else especially if they use strings.

Do you still have Balgrufs Axe in your inventory?

I am having the exact same issue and don't have the Axe in my inventory, I have disabled the only mod I would think would conflict "Better Quest Objectives" however this doesn't look to be a common error, and I'm starting to think my save is fubar