We just moved into a new house with a Kenmore Elite Ultra Wash Dishwasher 665.16572. I takes about 2 1/2 to 3 hours to run through its cycle. It seems to clean the dishes fine, but should it take this long?

... but should it take this long?
No, of course that is not correct!
I suggest you check the water pressure to start with. Is the tap fully open?
Also check if the filter is not blocking the incoming water.
Do you hear water coming into the machine and spray through the nozzles?
And check after 5 minutes from starting what is happening inside by opening the door : is there sufficient water?
Success!
As always : if you require more info, please let me know, with an answer to my various questions here.
If this solves your problem, please rate the answer provided! Feed back is always appreciated!
;)

Question - come to think of it by Kenmore dishwasher takes several hours as well. How long should a standard cycle take?