I've bought a handful of tickets through the Web site and never had a problem. My last purchased, I noticed, took about 10 days to post to my credit card -- I thought I had lucked out!

I will add, though, that I've never tried to change a ticket.
Now that I think about it, I had a PHX-IAH-DAL RT in which I purchased a PHX-IAH RT and a IAH-DAL RT separately, one through COOL and one through Travelocity (fare changed, don't ya know). I'm pretty sure the IAH-DAL segments done on COOL, but they were issued on paper tickets, for some unknown reason (before that, I hadn't had a paper ticket in years). I showed up at PHX without them (assuming I had been on an E-ticket, as usual).
At first, the HP agents said I'd have to buy a walk-up fare and then send in my other paper tix afterwards to get a refund. Then they called Houston and fixed it so boarding passes would we waiting for me when I got to IAH.
So maybe I did have a problem after all, but they fixed it without incident.