My 80-year-old mother sleeps almost all the time. Is that normal? Her doctor doesn't seem to be too concerned.

What you should judge by is what is normal for her, is the key thing. If she is sleeping more than is usual for her, it IS a cause for concern and, given the medical history you've outlined, I should go back to her doctor and ask him to have another look.

How is your mother when she is awake? Any other changes or problems?

Could be side effects of her meds.
Sadly, some doctors see 80 as a 'good old age' and are not all that concerned over her sleeping a lot.
What is sleeping 'a lot' to you? As we age, we need more times of rest, often. (Kinda like the reverse of childhood and infant patterns.)

Some people do indeed sleep a LOT (most of the day and night), and that should be taken up with assertiveness with her doctor. ( Are these pain meds, mainly? Heart meds? B/P meds? A combo of everything? Is there a warning label on the med(s) that states 'may cause drowsiness'? What is their opinion why of her sleeping so much? - they might not really know... What other options are there for her meds? Is this an indication of some other issue going on? etc...)
Keep asking until you get a good answer.

Could you give more information abut her condition? For example - Does she have any illnesses? How long has she had them? What particular meds is she on

What kind of meds?