Badly tuned generally refers to incorrect AFR (air-fuel ratios). These can not only cause lower power, but increase the amount of unburned fuel and other chemicals in the exhaust.
On some high performance cars you can even go as far as using the fuel's injection to cool combustion and decrease knock in the combustion cycle of the engine...sometimes this can lead to a richer AFR (more fuel in exhaust gases) which causes pollution.
Most (if not all) cars decrease the air/fuel ratio on wide open throttle, which ensures lack of air to burn pistons, etc., as well as cooling the charge to allow greater volumetric efficiency. Carburetors had a "power valve" to accomplish this, fuel injected vehicles usually have a vacuum hose attached to the fuel pressure regulator to increase fuel pressure temporarily. A fouled O2 sensor, mass air flow sensor or manifold air pressure sensor could throw off the ratios during normal operation. I'd venture to guess that "badly tuned" implies a misfire (probably a fouled spark plug) causing an entire cylinders worth of raw gas dumped into the atmosphere. This excessive fuel will melt down the catalytic converter which exacerbates the problem.
Indeed. That is why I specifically stated on high performance cars. High performance turbo cars, for example, at WOT generally aim for 11.2-11.8 (pending tuner preference etc etc, but ballpark) AFRs.
GDI cars have the capability of going extremely lean under highway speeds to drastically increase mpg and decrease emissions. This is the beauty of GDI.
These "badly tuned" cars could also have worn out valve seals/piston rings which can cause excess amounts of oil to burn during combustion, adding to the chemicals spewing out the exhaust.
On some high performance cars you can even go as far as using the fuel's injection to cool combustion and decrease knock in the combustion cycle of the engine...sometimes this can lead to a richer AFR (more fuel in exhaust gases) which causes pollution.