D. Remote Invocation initiated by Middleware
The question says "as quickly as possible" Outbound Message is Async & fire and forget pattern

D. Remote Invocation initiated by Middleware.

Using Remote Invocation initiated by Middleware allows for real-time or near-real-time address validation while ensuring proper order processing. It provides the flexibility to validate addresses as they are entered or modified in Salesforce, and the middleware can facilitate communication between Salesforce and the legacy Accounting system.

Here's why the other options may not be the best fit:

A. Outbound Message with a Callback: This pattern is typically used for real-time outbound messages, but it may not provide the desired speed and responsiveness in this case.

B. Nightly batch validating records modified the previous day: This is a batch process and would not be suitable for real-time validation, especially if timely order processing is a concern.

C. @Future method with an Apex callout: While it allows for asynchronous processing, it may not provide the near-real-time validation needed for order processing, especially if the 7-12 seconds per query is a concern....

It cannot be performed with a @future method because the context would be lost. The OM with a callback could be able to accomplish this.

No update on account, just validate => Can not use Outbound Message.

C. @Future method with an Apex callout.
An Apex callout using the @Future method is the most appropriate integration pattern for this scenario. The @Future method allows for asynchronous processing, meaning that the query to the legacy Accounting system can be executed in the background while the user continues to work in Salesforce. This can help to minimize the wait time for the validation and ensure that order processing can continue without delay. The remote call to the legacy Accounting system can be performed using an Apex callout, and the results can be returned as soon as they become available, allowing for quick and efficient address validation.

The answer is wrong. The correct answer is Apex Callout.