What is the correct term for the mouse pointer/nipple/joystick thingy in the middle of a laptop's keyboard?

The above device is generically called pointing stick:

The pointing stick (trademarked by IBM as the TrackPoint and by Synaptics as the TouchStyk) is an isometric joystick used as a pointing device (compare especially touchpad and trackball). It was invented by research scientist Ted Selker. It is present on many brands of laptops, including Lenovo's line of ThinkPad laptops, Toshiba Tecra laptops, HP business notebooks and on Dell Latitudes under the name of Track Stick. It has also been used on computer mice and on some desktop keyboards (as an integrated pointing device).

Apparently, the thing goes by many different names...

One of the most formal names is TrackPoint™-style pointer.

Other less formal or abusive names can be found on XKCD (16+, may not be safe for work).

There is no single correct term since there is no de-jure authority for naming of computer parts.

Different manufacturers use differrent names, you could therefore choose to regard the makers name for a thing as it's correct name

• IBM: Track Point
• Dell: Track Stick
• Toshiba: AccuPoint

See http://en.wikipedia.org/wiki/Pointing_stick#Naming_and_brands