I use a 50/50 mixture of alcohol (denatured if I have it) and water. That plus the microfiber gets fingerprints and grease off. Hit it with compressed air afterwards to clear off any dust or lint. I've never had a problem with the alcohol and plastic.
You can use a spudger (metal or plastic) to scrape it off. A putty knife, or any flat scraping utensil will work also. Just go slowly and work it bit by bit. The glue will ball up and can be peeled off. If you want to loosen it some, take a hairdryer and heat up the glue. That will get it to soften and release. Just be careful to avoid blowing heat directly onto the LCD, stick to the edges.