I"m not sure of the technique you are using, but you may find you get better results laminating the print using a hard and smooth sled. I use 1/4" plexiglass coated with Double sided mounting adhesive but leaving the protective paper in place, so the laminate is easy to remove from the sled. Also even pressure across surface is important. Depending on the laminator and the material, it is relatively easy to "bough" the roller of lower end manual laminators if using too much pressure, meaning the middle won't get enough pressure. If you choose to use a sled, it's best to make one that's nearly the same width as the rollers.
Here is a video from drytac that shows using a sled to apply facemount adhesive, to apply a laminate you would use the same technique.
Heat assisted laminators do help as they soften the adhesive. They usually only work at about 105 degrees or so. But you should be able to get decent results without the heat.
Sometimes the silvering will get better, but in my experience it usually won't completely clear up unless it is very minor to begin with.
As far as the dust, you may find it works better to wipe across the surface of the print with a
good glove to loosen those particles so they will actually stick to the dust roller you are using. Sometimes the adhesion between the dust and the print is quite strong and it takes some work to free it up. In the video (or the next one), you can see how he uses a flash light to spot pieces of dust, actually works pretty well.