What is considered dangerously high blood sugar and what are the symptoms?

No exact answer.: Depends on situation. In an uncomplicated case a bg of 600 or so will do nicely with some diet restriction and increased fluids. I have seen patients with bg in the 1000 range with relatively few symptoms. The symptoms of very high bg are generally related to marked dehydration. Feel lousy, thirsty, hungry, headache, abdominal pain, blurry vision, etc.

>300-400: Once you start getting above the 300-400 range of blood sugars, a lot of different things start to happen. You kidneys may start to purge sugar, so it shows up in your urine -- this action contributes to dehydration. You body metabolism changes such that unused sugars turn into ketones which change your whole system more acidic -- you don't want diabetic ketoacidosis! (among others) get insulin!

Depends: It depends on what other associated symptoms there are; if you sugar is only moderately high, but you have signs of severe dehydration and/or dka, this would be a dangerous level.