As are most things in Yate, the Title Case functionality is totally configurable.

Firstly, I've noticed that trying to change something in CAPITALS to Title Case doesn't do anything. I have to go from CAPITALS to something else, (I usually choose Sentence case), then to Title Case which does the trick.

Yep, every Title Case algorithm handles words already capitalized as exceptions. Yate has a mode called lower-Title case. About 99% of the time, this is what you want. It converts the text to lower case and then applies the title case algorithm. Basically it gives you a clean slate.

I'm not sure if this is a bug? It feels like it should work.

The way Title Case works is not a bug. It's following the most common set of rules.

Secondly, is there a way of making it a "strict" title case (so that "Planet of the Giants" becomes "Planet Of The Giants" or "Diary of a Madman" becomes "Diary Of A Madman")?

Use the Capitalize function. It's available on the Multi Field Editor's Case panel and in action statements.

If you go to Settings-General-Title Case, you can set the title case algorithm.

You could still use lower-Title case but you'd have to set up those words and other like it as exceptions. If you don't BBC will become Bbc.