why does latex report errors when using styles in a tikz pgf picture?

The problem is caused by the empty line after you opened the tikzpicture environment. Note, that an empty line usually means a paragraph break, so don't use it in the document code just because of readability. If you would like to use (nearly) empty lines for separation, set at least a % into the line to comment it out.

It works this way:

\begin{tikzpicture}
  [Karl's grid/.style ={help lines,color=#1!50},
  Karl's grid/.default=blue]