Thanks @darkhorse20, your feedback on this thread is very helpful.
I was incorrect in my previous reply. Did another line by line compare of the source code of a "bad" and "good" page and indeed for the "bad" pages, the cache is not generating the Ubermenu specific html markup, hence the crappy looking menu.
What I don't understand (and haven't had time to investigate), is why aren't the cache plugins not catching the Ubermenu html markup and caching that, but caching the default WP menu markup instead? Is it because that particular page was loaded in an incompatible browser (i.e. IE6 or IE7) where Ubermenu doesn't load at all? Or is it related to how Ubermenu is implemented (therefore cache being created before Ubermenu has been initialized in some cases)?
The mfunc solution looks legit and I will try that, but my end goal is to remove Ubermenu completely and write my own clean markup instead.