Nuther question: '03 GT --- what's with the RPM hanging between gears?

The car I recently drove (2003 GT, 65K miles, 5-speed) was quite slow and the RPM wouldn't drop when you hit the clutch to change gears. It would fall, but only after about 2 secs and then too slowly. It made for a very annoying drive.

Is this something wrong or is it the way they all are?

Thanks!