CHEAP power supplies

That is interesting.  What is that?  Do you have a link?

here the wiki of ferrite core. http://en.wikipedia.org/wiki/Ferrite_core

How would I attach one?  Which one would I buy?

RoHS is not a company.  It is a standard http://en.wikipedia.org/wiki/Restriction_of_Hazardous_Substances_Directive

You can experiment with the ferrite core idea by trying one of these http://www.radioshack.com/radioshack-snap-together-ferrite-choke-core/2730105.html and seeing if it improves the mouse.

OK, I get it now.  Very interesting.  Let's say that does work for the power supplies with that problem.  What kind of keywords might I employ to ensure that I order power supplies without that issue in the future?

Probably a search won't do anything for you.  Instead look at reviews of the product especially if it is sold on Amazon.  Look for the worst reviews and see what they complain about.  Also compare the number of excellent reviews to the poor reviews and see what the ratio is.

If the mouse has a USB receiver, does it make any difference if you use a different USB port?

If it were my laptop I'd bite the bullet and get a different power supply. If it's creating that much noise/interference I wouldn't be confident that it wouldn't eventually cause damage.

It is the touchpad that is jumpy until I unplug it.  I tend to agree with you about getting a different power supply.  The trouble is that I have had this happen more than once.  I don't want to pay retail so I am trying to figure out how to ensure compliance before the sale.

if you end up buying two or three power supplies until you found one that worked properly you would end up paying more than a retail unit would cost. Usually the manufacturers parts are the best for their systems, as they were designed for each other. This is why they are more expensive and are usually of a better quality, less magnetic interference, etc. If you insist on purchasing a generic adapter always, ensure that the voltage and amperage are exactly the same as the original adapter designed by the manufacturer. The wattage can be different, as a higher wattage would charge the battery faster. I remember when I used to work for Dell they had two different wattage adapters one would be for a powering docking station and one for plugging directly to the laptop, but the higher wattage one from the docking station could be used to plug directly into the laptop, where as the one designed for laptop only use could not be used on the docking station, not enough wattage.  Both adapters looked identical had the same voltage and amps but they both had different wattages. So be careful what you buy.

The voltage needs to be exactly the same, the possible Amperes of the Power Supply can be bigger than the original one, the Laptop will only draw the current it needs not more.
I also tend to buy an original powersupply as a replacement, or a used one from a broken laptop or same model/brand.

my experience with 3rd party power  supplies for laptops was just bad
nonen did work as expected...

Perfect answer.  All these years of being utterly confused about this and here is the conclusion that we came to.

When buying supposedly compatible power supplies, the number one thing we look for now is whether it is a 3 prong plug or a 2 prong plug.  The ones we seem to be having problems with were the two prong plugs which are not as thick as the two prong, not to mention that they have no grounding.

Simply choosing power supplies with 3 prong plugs seems to be at least part of the solution, and in our case, it has been a big part.