A decent TA will handle everything. I send an email saying "I need to be in Singapore 9AM Friday morning, Tokyo for Wednesday 9-5, and back to London ASAP after that", and receive the right flights. I'll be waitlisted in multiple classes if the flight is full, and backup flights will be booked in case.

If a flight is cancelled and BA shift me to another flight, I'll get an sms from the TA even when BA don't bother.

When a flight from Moscow looked like it would go tech last year (hadn't been annouced), and despite having already checked in, a quick phonecall to the 24/7 line and two of a few seats on the next flight were booked for me and a colleague. A couple of people using ba.com found they couldn't do anything.

If you book enough your company may get a rebate from BA, and even occasionally lower "corporate" fares.