I've seen on some other modding sites that they polish the perspex with a flame.
I tried something this weekend with some acetone. I tested a piece of perspex by engraving some pictures into it. The 'spex had that white residue from the dremmel and I wanted to remove it. I don't have a blowtorch but I found some acetone in the garage. I heated up the 'spex, but not for it to bend, and then poured a little of the acetone over a small area. At first I thought it would just eat away the 'spex but it didn't. I was left with no white residue but the acetone dried and left a little bit of residue. It looked good though and I was able to get the acetone off the perspex and it looked really good.
BTW I was at maizeys the other day and asked what the differences are between plaxi glass and perspex and well I was surprised.
Persex is made in South africa and has a less even surface than plexi which is imported from somewhere (Germany I think they said). Plexi is made at a lower tolerance than Perspex. Example. The surface of perspex has a tolerance deviation in the thickness of say 0.1mm while plexi has a tolerance of say 0.001mm. Perspex and plexi are made out of the same chemical compounds and such. Perspex has more colours available because it is made locally and its expensive to import all the colours.
Google, you'll find plenty on the topic.