So, here is my list of things I go through...
Make sure the SWU is listed first in the PNR. You can see this online when you look at your flight as it should list the wait listed flight first, then your coach seat. If not, call to adjust.
Make sure they not only list the SWU but the redemption code in your PNR. This isn't anything you can see, you just need to ask.
When your are under 24 on all of your legs you are trying to upgrade I would then check in, this should start the process of moving you from the wait list to the upgrade list. In my experience this is where you will find out if everything works out. If they did their job you should get your BP's and check your status on the upgrade list. It should be fairly high, 1 or 2 I should think unless you have others using SWU's on your flight. If your listed higher on the UG list chances are you did not process the SWU and you are on the list for a medalion upgrade instead. The way to fix this is to call and have the agent validate the cert processed and that your upgrade priority is UP2a for diamonds or UP2b (I think) for plats. If you get someone that has no idea hang up and try again. I find I have the best luck with SLC agents with SWUs.
Also, if the UG list says see agent, its messed up. Some phone agents will tell you that is normal because you used a cert but that is not the case. Keep calling the medallion line until someone on the phone goes, "oh I see what is wrong..." Once they say it is fixed validate by checking the UG list yourself. Keep them one the phone until it looks correct.
A little known fact one agent told me, agents can see the status level of people on the UG list. Any agent that understands the UG order can quickly see if you are in the right spot.... they key is finding the right agent.
One other thing... if you are in a situation where an SWU processed for one leg but you are wait listed for another... (this happened to me once). You may need to call T-24 to have them actually process the cert. In my case the online system would not process it and thus I could not check it. Once they redeemed it over the phone, online check in worked and I was placed on the UG list properly.
Hope this helps.... just be prepared to a me phone calls and don't argue with an agent that does not understand the process... it will get yo nowhere... :-)