How do you find out if a dementia home's staff are actually trained in dementia care?

Hi, thanks for sharing this, it's a really common worry and a fair question to ask.
You're right that there's no legal requirement for staff to hold dementia-specific qualifications beyond basic induction training, CQC checks that training happens, not that it covers dementia in depth. So asking directly is a good instinct, and there are a few specific things worth asking rather than a general "do staff have training":

• Ask what dementia-specific training staff have done, by name (e.g. dementia awareness, understanding behaviours that challenge), not just "in-house training"
• Ask how often it's refreshed, one session years ago is very different from ongoing training
• Ask to see the home's last CQC report and look specifically at what it says under the Effective and Caring sections, staff competency and understanding of individual needs usually comes up there if it's a real weakness - You can access that report from the listing on this site.

On the moving question, that's a genuinely difficult one with no universal answer, it depends a lot on how settled he is and what's actually not working day to day. Worth writing down specific examples of care plan points being missed, since that's concrete evidence you can put directly to the home's manager, and gives them something specific to respond to rather than a general concern they can brush off.
Hope that helps a little.