Dear Splatz
As physiotherapist myself I have to say that keeping the body as physically active as possible is beneficial in many ways. Pressure sores, blood clots, muscle weakening, reduced joint movement and chest infections can all be caused by a lack of mobility. Simple exercises that can be done in lying, sitting or standing can help, but walking is probably the best form of exercise. However, it is obviously very difficult to get someone with dementia to follow an exercise regime, but if you are interested it may help to contact your Father's GP and ask for a referral to a mental health physio who should be able to give advice.
It is an unfortunate reality that most (not all) nursing homes have little room to move, and even if there is space, not all of the staff are happy to give clients the opportunity to move around. In many NH's that I have visited, I have left instructions for staff to safely walk patients but the advice is ignored as it is easier to put a person in a wheelchair and wheel them around. This is especially frustrating when you are trying to keep at least a tiny bit of independence for the person involved, which is then taken away due to lack of time on the staff's behalf. I would recommend speaking with the staff about your Father's care plan to ensure that he is allowed to walk as often as possible if it is safe to do so.
At some stage walking may become very limited, as you may have seen on other threads. Again, I would reccomend speaking to a GP to get as much help from physio's and/or occupational therapists as possible.
I haven't seen any evidence to show that exercise can help with the symptoms of AD, although it can reduce signs of depression in early stages. I hope my ramblings have been of some use. Take care, love Kate x.