Unfortunately this is very common in the industry. Bugs and dirty water get on the shield and leave spots of mold beneath the surface. It is extremely difficult to remove. As if taking off the shield a fraction of an inch at a time is not bad enough, the glue residue is very difficult to remove. I did about 2 square feet once and it took 10 hours. It is important to remove bugs from the shield every day. 

There are several solutions available and you tube videos.. A company in Tampa Ugly Shield Rover

seems to be the best. They can do it or will sell the chemical necessary if you are brave enough to try it yourself.