In doing some mock drafts, I have the possibility of trading picks with a couple of teams during the real draft and I don't see the DD adjusting the Best Value Pick to match my team. It is showing the team the computer thinks is on the clock.

For instance, if I am team #1 and trade picks with team #8 in the 5th round, it is showing the Best Pick for team #8 instead of team #1. How do I make the adjustment on the fly?

How are you trading picks? With the File->Setup->Pick Order?

If you are on the clock... and then trade a pick... you will have to click the update button to get the new results.

No, I was trying to do a trade after the draft had started. I have tried changing the team in the Draft Status window and then hitting update in the Best Value Pick window, but nothing changes. What else can I try or does the software simply not have the ability to do that?

Try the File->Setup->Pick Order... and swap the picks there. It should work!