Actually proof of residency only applies to the SF Neighborhood Free Days days. Certain neighborhoods will be able to get in free on whatever dates listed (great idea by the way, but it sucks for people who have friends living in different parts of the city!).
Regular free days are different. There's probably no list of these days because it's just every third wednesday of the month. It's open to everyone and you don't need to bring any proof of residency.
I hope that cleared things up a little..
Smellslikeemo is correct about the proof of residency on Neighborhood Free Days, and how it sucks that friends go in groups and not together. For the Mission District residents it is free on May 1, 2, & 3. I hope to see everyone in my neighborhood there.
As a rule, get there early. They open at 9:00 and a line will have already formed. Upon entering, have one person in your party stand in line for the rain forest while someone else stands in line for the planetarium to get passes. Planetarium passes are usually gone by 11am!
The rest of the museum can be seen after these two major attractions.
Thanks merlin for that advice of how to stand in line. Now Im thinking it may be worth not going on a free day if one can afford to pay since the lines will be even longer on a free day.