What is my responsibility concerning my mom's will?

Those who are Power of Attorney cannot update any legal documents of others, such as Wills.  Only your Mom could do that, but that doesn't sound possible now.

Keep a log of what date you started to clean out Mom's apartment.... when you notified your sister... how many times and how you notified her.... what items that were in the Will for sister but sister never came to retrieve any of the items.   And anything else you can fill into the log.

Oops, I just noticed that 97yroldmom above was thinking the same things. 

You can't update the will. Only your mom could do that. It's too late for her to do it. If your moms assets are gone it is my understanding that there is no need to probate the will. If you didn't send sister a notice in writing go back and look at emails, text messages etc and make a diary or record of your efforts. Dates and content or copies. Then if anything comes of it in years to come, you will have that to help your sister understand the decisions she made regarding her inheritance.

Thanks pamstegma! I did set a deadline. But she's my sister, it was over the phone. I also waited 5 weeks beyond that deadline before letting the stuff go. I don't think there's a legal issue now. My attorney said it's "a gratuitous transfer with no consideration based on the red line contingency of my mother's death." I get that, but what about after her death?

As her POA, I *could update her will. Just wondering if that would make it easier for me after my mom dies.

My sister has never come to see my mother in the nursing home. She spent her life asking mom for handouts, then when my mother finally put her foot down (sis was approaching 50 and needed to be responsible) she turned her back on my mom. Limited her calls to 5x a year (new years day, her birthday, mother's day, thanksgiving, and Christmas). Came to visit a handful of time in 15 years, always with friends to use my mom's place as a NY crash pad. Completely ignored us, ate my mom's food and didn't clean up after herself. But I digress...

In short, sis does not care about my mom. But she sure cared about mom's 40 year old bedroom set! She has not spoken to me since February of 2015 when I gave back the apartment. As an aside, she never chipped in for the rent and utils I paid to hold the apartment after mom was gone, as she had offered. She hung me out to dry to handle my mother's illness and placement in the nursing home all by myself. Nonetheless, she is furious, and not above attempting a frivolous suit. Just wondering if the update would be a prudent thing to do. Updated circumstances, updated will. I donno...

Hopefully, you notified sis in writing, setting a deadline for collecting things. I had asked my SIL what she wanted from the house. Nothing. So we cleared it out, gave things away and filled two dumpsters. Months later she was howling about not getting anything.
As for the assets: The first part of the Will instructs the Executor to pay all bills and claims against the estate. In NY you must wait 7 months for bills to come in. You only divide and distribute what is left after the waiting period. In many cases, where the parent has gone to a nursing home, nothing remains. You do not need to update the Will.