The key to cutting plastic is to do multiple passes. Let's say you're doing a round over. Make 3 or 4 passes, dropping the bit. Let the bit and part cool and just shave a couple thousandths off on your final cut.
Always use a conventional cut, (blade cuts into material) vs a climb cut, (opposite and dangerous with hand held tools).

Should be clean and melt free.
Pretty much the same thing if making a dado. Keep your cuts around 1/16" as you drop down. As you get accustomed to this work you can get more aggressive.
When flush trimming, rough trim your part as close to the completed size as possible. Then trim.
One of the most important parts when you're learning to hand held rout, is to hold the router steady and firm while keeping firm pressure down to keep the tool perpendicular.
Always use a conventional cut, (blade cuts into material) vs a climb cut, (opposite and dangerous with hand held tools).

Should be clean and melt free.
Pretty much the same thing if making a dado. Keep your cuts around 1/16" as you drop down. As you get accustomed to this work you can get more aggressive.
When flush trimming, rough trim your part as close to the completed size as possible. Then trim.
One of the most important parts when you're learning to hand held rout, is to hold the router steady and firm while keeping firm pressure down to keep the tool perpendicular.