Ticket returns are common for most performances so keep checking the website or by phone.
The 'authorised' ticket vendors listed on the ROH Tickets page seem to have quite a markup in price, but not nearly as much as rogue vendors who should be avoided at all costs.
The Friday Rush for buying tickets for the following week's (Saturday to Friday) performances starts at 1pm on Fridays. There are 49 tickets per show and only 1 allowed per person for any show. This system was introduced about 18 months ago when the old ROH box office was closed because of large scale refurbishments. Previously, day tickets - 67 I think - were sold each day at 10am with priority seemingly given to people who could queue at the Opera House. This disadvantaged people who couldn't queue but was very useful for London visitors as, if they arrived early enough, they were very likely to get tickets. However the current arrangement is more equitable. Friday Rush tickets disappear at an alarming rate! I think it is possible to queue for Friday Rush tickets but I have never done this.
The rules about ticket returns at the ROH seem to be in a constant state of flux. The current situation is that unwanted tickets can be returned for resale by giving full details by email or phone. It is no longer necessary to return the actual ticket. Returned tickets will only be put on sale if there are no other tickets in that location and price band available. The refund deduction for a successful sale is £4 since the end of last season - previously £2. In my experience returns may sometimes be accepted on the day of performance. Some of the information on the ROH website Tickets page is out of date in varous respects.
Helpfully, the box office will hold tickets that you want to leave for someone else to pick up. A very useful and longstanding service. The Tickets page says that the person collecting needs to bring a form with details of the ticket(s), the person leaving them and the person who will be picking them up. This rule seems to be more honoured in the breach than the observance.
Hope this information is correct!