You should look for how they decide to portray different scenes or characters. For example:
Lear
Cordelia
the other sisters
Kent
Gloucester
Edmond
Edgar
The Fool
the storm scene
the ending
All through the play there are choices to be made as to how you wish to portray each character and each scene. They can all be portrayed in a different way which will affect the meaning. For example, does the production you are watching show lear as a weak old man or as a strong fiery man? Make sure you have your own opinion of each of these, and that you refer to it.
Take notice of any lines the production excludes, for example many exclude Cordelia's asides in the first scene, taking away her justification for saying 'nothing'. This is useful to portray Cordelia as a stubborn character, similar to her father, rather than as the personification of virtue.
Take note of costumes, this gives a clue to characters, also to setting, lighting, mood etc.