For applications like opera, firefox the entry in the task manager used to be the current tab title. But in my arch linux kde 4.3.2. At some point it stops updating the taskbar entry. The entry there will be some old tabs which I have changed or closed.
I noticed the same behavior for both firefox and opera.

Does the Window title contain the incorrect name? If so, is the window decoration responsive?

Window decoration is responsive. Now that you mentioned I noticed that Window title is not changing, but task bar entry changes. But this behavior is always not reproducible.
I saw both ways
1. only task bar entry getting updated not title
2. only title changes not taskbar entry
3. both changes correctly

When the window title fails to update, does forcing the decoration to repaint cause the correct name to appear? ( You can do this by right clicking on the decoration at various points )

This is likely either a KWin or Plasma bug.

Its difficult to reproduce the window title issue. As that was the first time I also noticed.
But system tray entry not being updated I can reproduce.

If 3d desktop effects are enabled, try disabling them.

I actually have a similar problem when one half of the title is new and the other is old (right-clicking the titlebar fixes that). I might take a screenshot it happens again.

I have that problem occasionally also.