I think the most valuable skill to have at a playtest table is the skill to break a game. All the other skills are very important but as a designer, I always appreciate it when a player break our game. Everyone gets blind spots when they see the same game over and over again.
When I leaned how to break our own games, I think the first thing was to remove any notion of wanting to win the game and find a strategy that no one else at the table is using. Another take on this idea is to try the same strategy other players are using and see how the game reacts. I look for the limits of the game and I want to try and hit them. Think along the lines of resource limits, hand sizes, a fast character with no armor or a beefed up character with no speed. What happens if I try to horde a lot of resources, what happens if I try to play the entire game spending resources as soon as I get them? What happens if I hold on to a full hand size? Do I have options through the whole game, or do my cards lose their value as I am not playing them? Can I find a character that is over powered compared to everyone else?
These are just a few examples of the kinds of appraoches you can apply to a game when you are testing it.
The more published games you play and the more prototype games you test, you will be able to identify the weak points and put them to the test. Not only are you allowed to go outside your normal style of play, you are helping out the designer and the game in the best way possible.
If you have any comments or questions, leave a comment here or email Chris at firstname.lastname@example.org