The problem is with the MAC address filter. DIR-825 works okay with MAC addresses that start with 00:
My iPad's MAC address starts with D8: so we have an issue.
Without MAC filter, iPad works fine. But if you try to save iPad's MAC to the filter, you will get an "invalid MAC address" error. BTW, I am using 801g with firmware 2.02NA.
If I don't get a firmware update soon, my DIR-825 is going back to Costco.