Officially you might need to get your ticket reissued (or revalided), but I've never done this, and never had any problems. (reissueing a handwritten paper ticket is not easy or quick!).

As long as you have a coupon for the correct route and a reservation for the flight you want there should be no problems. If you have a eticket things are different, but a reissue is much easier in that case.

There are definitely problems between the reservation systems of the different airlines, but the reissue of a paper ticket will not solve this! (For e-tickets this is different, and can cause problems if the ticket is not properly reissued.) It is best to check with the airline you are flying with to see if there are any issues with the reservation. On my AA issued paper RTW ticket my LAN flight reservations were canceled 4 times! The first 2 times I had the reservations reinstated by AA, the last 2 times by LAN. It was only fixed when I found a competent person at LAN and I convinced him to enter the ticket number manually in the reservation! Cathay is also known to automatically cancel reservations if the ticket number is not properly entered in the reservation.