I think the budgeting capabilities online and in the app could be improved a lot.
One of the things I would find particularly useful would be to have calendar based budgeting, similar to what Pocketsmith and Calendar Budget offer. It's essentially a calendar view of your budget, with recurring transactions projecting your balance. Income increases, recurring payments such as mortgages, etc. decreases. Pocketsmith allows for multiple bank accounts to be tracked on the same calendar.
What is great about this feature is you can see exactly how much you will have (or not have) on a given day based on your current plan of spending/earning. It is a good visual motivator to NOT splurge on dinner, and also it's great to see what the long term impact is if you can reduce your phone bill $50/mo.
As transactions come in, it replaces the projected/budgeted amount in that category day by day. Ad hoc transactions also land on the calendar as you spend/deposit.
I have been looking for a tool like this for a long time and I think that it would be very helpful to incorporate it into the overall BECU experience.