This is the term we want here; you might say "as if it had overspray, like when paint is oversprayed", or something like that; there are several ways you could put it.

The pictures of the paintwork in the forum you posted do look as though the problem is the texture of the paint, but if you read the posts it's clear that "briseado" means that the car has been sprayed with extraneous paint. Note that it affects the windows, not just the paintwork:

"tengo briseado los cristales del auto con pintura"
The car was spattered with paint when it was parked: "no hay nada peor que estar estacionado en el lugar equivocado a la hora equivocada"
Someone recommends removing the "briseado" with a clay bar.
http://www.meguiarsenlinea.com/forums/showthread.php?607-¿CO...

This meaning is confirmed by other comments:

"Tengo un problema, resulta que mi vecino se le ocurrió pintar su portón con pistola de pintura, y ha briseado toda la pintura de mi rav4 , la pregunta es ustedes creen que con cera se quite esos puntitos de pintura?"
http://rav4.mforos.com/1078749/7899886-briseado-de-pintura/

http://autocare.mx/foro/index.php?topic=378.0

In English this is known as "overspray":

"Overspray
The fine mist of paint on areas where it is not wanted (glass, moldings, other painted surfaces, etc). The distinguishing mark of a vehicle that has been painted or had body work done."
http://www.motorera.com/dictionary/OV.HTM#Overspray

"Cleaning paintwork suffered overspray
Hello all,
I hope someone can help me. I parked my pickup near where I was working on a factory overall, which included other personnel spraying external fittings. The wind must have carried their spray as the pickup is covered in a clear 'gritty' substance like varnish."
"i would ask a bodyshop to give you a proper cut of the body as it sounds you got a fair bit of overspray"
"Clay Bar - works a treat and what it was originally designed for. "
"Another vote here for the clay bar."
http://www.honestjohn.co.uk/forum/post/index.htm?t=56056

"will a clay bar remove minor paint overspray?
i spent time in a hotel. we paid for underground parking. when we checked out, and tried to drive out, i couldnt find the entrance/exit. the lot had sheets of plastic up, because a crew was painting the garage. i drove towards the noise and work lights, and i found the crew painting the area around the entrance. [...] i washed the car, and yup,, overspray"
http://forums.pelicanparts.com/off-topic-discussions/411898-...