Is it common for people with dementia to falsely accuse family members of doing things to them?

Yes don't worry about it, my mother is 103 and she has short term memory loss repeating thing she just told me, i don't tell her what she's doing as she doesn't realise it, she blames people for taking her glasses, she picks up thing that don't belong to her and the nurses have to go to her room and take them back, she tells me i look like a Buda, last time i went to see her she said who are you, i said you know who i am and she said why are you wearing that stupid mask, look at the size of you, she often says to my brother and i, i suppose you've spent all my money, little does she know that the little money she had is long gone paying for the home she now lives and my brother and i are paying for her to be able to stay where she is, 

next time i see her she's in a really good mood and so happy to see me. i just remember what a great mum she was, she was a wonderful lady and that memory is good enough for me not to worry about the things she now says.

I am not yet quite 80 but I know that my memory is causing issues for me and others.   I don't like it but can do nothing about it.  I've spoken to my sons about it, they understand and have noticed some inconsistencies. I preferred to discuss it myself with them before they began discussing me with others behind my back. It's now out in the open and I know that, if I live long enough, it will become a bigger problem. For that reason I don't want to live to almost a hundred like my mother did. Once the mind has problems I think it's best that the body follows and we let go of life - IF that's possible.  I'm not condoning suicide;  I just don't want to be kept going for the sake of it.  I'd like to go gently and reasonably soon.

Yes it is very common. Try not to be offended. They don’t remember what they did with it, they are listing part of their identity and memory so they will sometimes say terrible things. Sometimes become an entirely different person. You have to love them anyway and hope for the moments of clarity where you see them as they really are

Yeah, pretty much. Ask her doctor what to expect to get from her.