The 'mouse' keeps flickering, as if I am shaking the wii remote rapidly.

1. Make sure the mouse is fully charged. The underside should have a red flickering light if it is working properly. If not you need to change the batteries.

2. Plug the USB dongle into the computer. The blue light should light up and flash rapidly as you move the mouse around. If it still doesn't work you need to re-sync the mouse with the dongle.

Turn the mouse off and back on again. Hold it near the USB dongle.
Push the blue button on the dongle. It should flash steadily. Push the reset button on the bottom of the mouse. The blue light on the dongle should start flashing rapidly and your mouse should now work.

take the back off and replaces the battery or it's time for a new remote. you can Find Cheaper Ones on ebay and Craigslist

Shake the wii nunchuck for a spin attack like you shake the wii remote for a regular attack.

Try shaking the Wii remote instead of the nunchuck OR shake the nunchuck harder

Mario isn't supposed to spin at first, he gains a star friend that enables him to spin. To spin, just shake the remote from side to side. If you have gotten the star and he still doesn't spin, make sure your batteries in the remote aren't too low or try resetting your console.

First, I would check the batteries in the Wii Remote. Low batteries will make the Wii Remote signal flicker. After that, I would re-sync the Wii remote by opening the back of the remote and pressing the sync button, after you turn the Wii on, of course.

try preesing B to do the other thing

shake your wii remote and nunchuck when you get wobbley and shake your wii remote and nunchuck like a trians wheels to go and stop shaking the wii remote and nunchuck to stop

You have to be holding Wii Remotes in your hands for it to recognize the motions. Check the instruction manual for a description of exactly what it wants from you in terms of the kind of motion. It's probably just looking for you to shake the remotes around. My understanding of DDR Hottest Party is that the hand motions were not very well implemented, but I haven't played it myself.

Could be power supply related or the hyper board, Toshiba p/n# 23148017... Cycling on/off is the TV's protection circuit going into shutdown to keep from causing real damage. Get it to a shop and have them estimate it.