Address

No. This should not affect your return. While it is ideal to use a more permanent address on your return, the IRS typically does document matches related to tax ID numbers, such as the social security number, and the information reported as dollar amounts. Be sure to update your address with your employer going forward so that you can receive the appropriate tax documents in subsequent years. 

You can also notify the IRS of a change of address in the event they should need to reach you.

IRS Change of Address

When taking Child Care Deduction the program rejects the state as AP on APO address for Child Care facility. I have changed the address on personal section to Military APO address.

There are no known issues with what you're describing.

Perhaps you could delete and re-input your information to see if this will correct the issue.

In TurboTax Online,

1. Click the Federal tab in the left pane.
2. Click the Deductions & Credits tab near the top of the screen.
3. Under Your tax breaks, you should see Child and Dependent Care Credit.  Click Edit/Add to its right.
4. Proceed through the interview questions until you get to the Here are your care providers. Next, we'll get your expense info page.
5. On that page, you'll see your care provider's name.  To the right, you'll see a trash can icon -- click this to delete your information for this care provider.
6. The same page will regenerate, and you can click Add a care provider to start over.