Gosh, it's so hard isn't it? I'd feel the same with a family member too if I overheard them being spoken to like that. If I were you, I would definitely move him closer to you so you can visit more often, which should relieve some of the 'unknown' feelings/suspicions.
I would not have any issue with someone installing a camera without my knowledge (sometimes I often wish there was one, as we take a great amount of pride in the way we care and love for the person we look after, even when it has been extremely awkward or difficult at times), but that is in a private home setting, and I guess there are more legal issues in a care home with multiple staff and residents.
That said, on a very personal level, I'm of the firm belief that a potential victim/vulnerable person is always the one who should be protected, so on an ethical level, if you truly suspect abuse of a PWD, especially a direct family member, you should be within your personal rights to monitor the situation without the carers knowledge, regardless of the rules and regulations (how else could you prove it one way or another). But I would not use that monitoring to nitpick or micro-manage anything, only to monitor and check for a few days to be sure of no abuse (verbal or physical), and I would also be prepared to accept any legal consequences at that stage - that's just me - I think welfare is more important.