ScriptEngine.Execute can throw many unexpected exceptions. Here are the types of exceptions it can throw and the code snippets used to trigger them:

ArgumentException

new ScriptEngine().Execute("if(5 .toString(3)==0)(0)");

ArgumentOutOfRangeException

new ScriptEngine().Execute("new Date(0,0)");

IndexOutOfRangeException

new ScriptEngine().Execute("delete[].(0)");

InvalidCastException

new ScriptEngine().Execute("({[0](");

NullReferenceException

new ScriptEngine().Execute("function a(){for(a=0;a<0;0++)0}");

Found via SharpFuzz.