On virtually all newer televisions and in particular Mitsubishi televisions there is a problem with interference being emitted by the switched mode power supply.
The common symptom of this 'fault' is snake like dotted 'S' lines on channels 2-6. It doesn't matter if it's cable, antenna or satellite(channel 3/4), this symptom can occur.
The common cause of this interference being allowed into the tuner is cabling. The super cheap 'suitable for garbage tie' cable that comes with even the most expensive VCR's is the culprit in most cases. The second is a set of rabbit ears the least common is an open or high resistance to ground connection (usually at a connector) on the incoming cable line.
To fix this there is only one reliable solution. All cabling must be hand made RG-6 cable. Make as follows:
If the cable company doesn't waterproof the outside connectors, Radio Shack sells a 'sealing tape' just for this purpose. Most cable companies use self sealing 'o-ring' connectors.
(From: Jeroen H. Stessen (Jeroen.Stessen@philips.com).)
There is also interference from internal microprocessors and digital text generators (on-screen display, close captioning, teletext). And with 100 Hz digital television there is a wealth of sources ...
Using only high quality shielded cable as described above seems like really good advise, FWIW I'd like to second that. I wish that everyone would take antenna cables as seriously as you.
Generally, double-braided cable (using copper foil for second shield) and coaxially constructed connectors are recommended. But I think that the hand-mountable F-type connectors (Radio Shack) would be equally good, though less robust, if mounted properly.
As far as antennas go, a decent rooftop antenna should always be better than whatever rabbit ear construction you might think of. In this case, distance counts too, the antenna WILL pick up interference.