Mentally Disabled woman across the street is unsupervised for days on end. What can I do?

Oh, the police can do something. In fact, that's probably the best thing to do. They'll get senior social services involved in a heartbeat.

I would call APS(Adult Protective Services) instead of the police

I'd call them both.

Unless you can talk to the caregiver about what's happening while she is away.

There could be many reasons the caregiver leaves the woman alone. They could be a wellness nurse from a health plan, a well meaning relative who has taken it upon themselves to try to help....My friends sister has attacked her on occasion and often yells at her to "Go away. I can take care of myself." The neighbors see her as the "caregiver", but there is no formal arrangement. None of the other 3 siblings do anything. Many haven't seen the mentally challenged sister for decades.
The main thing is to focus on the woman needing help and also on protecting yourself and your family. It may seem mean to call the police, but you cannot make someone admit themself for care. The police should know that the woman is doing things that could harm people in your neighborhood. The police have the power at least to get them committed for observation and hopefully then a caseworker would get her some more help.