For symbols, I play with varying methods, but usually just put a dot when I've looked at the array, an x when I've completed the array, and a small square when I've reached a point in the array where I have there is a known or a pair in every square, but it will take information from another array to determine which pattern is correct.
For columns, rows, and squares, I list the symbols which remain unassigned.
Within the grid I mark singularities, twoshares, and pairs which are completely within a square (whether they are pair in the long set that intersects the square as well or not.) Outside the grid I'll sometimes underline the symbols which have only two possible spaces in that row, column or square, but I often leave that until I'm stuck.
Here's a picture with one example for each side of the grid. (The blotches in MC are a goof.)
As you can see I've done the 1s, row Mm, column Ll and square BC, so far. But because I messed up this copy of the puzzle, I started over, showing how I'd actually be doing all this in pencil.
I'll upload those pictures tomorrow.