There is no requirement that a POA document be filed. However, some people do file the POA document with the county's recorder. In King County, the Recorder's website for online record search is: http://www.metrokc.gov/recelec/records/default.htm .
A person with mental incapacity would not be able to sign an enforceable POA.
If you suspect that your mother is being abused (whether physically or financially), you can report the abuse with DSHS. Its website for adult services is here: http://www.aasa.dshs.wa.gov/ .
Someone with dementia lacks capacity to sign a POA. Also, there are two kinds of POAs. One for financial / legal matters and one over health care issues. The exact answer to your quesiton depends on the nature of their claim. Are they spending money out of a bank account? Are they making health care decisions?
Legally they do not have to present you with any paperwork. They need to present it to the bank, health care facility etc. You could ask the institution for a copy but they probably don't have to give it to you either. WA does not require POAs to be filed with the court. One curious thing about financial POAs is that many institutions stop taking them after 5 years.
You could always try the Soprano approach. "Show me a copy of the POA or I'm going to..." One course of action is to launch an investigation through a guardianship process. A little spendy but very effective. If you do not suspect abuse but something just doesn't seem right you can contact an elder law attorney.
Visit http://pro.wsba.org/, type in your city name and select "elder law" from the area of practice drop down menu. This will bring up a list of elder law attorneys in your area.