Two things may be at work here:
1) Convergence is somewhat related to the Earth's magnetic field. That is to say, if you move the TV at all the convergence will be off. Furthermore, convergence relies on precise alignment of the RGB guns in the TV ... if it gets bumped, convergence may be thrown off. Also, convergence will drift by itself over time. User-level convergence will help, and a service-level convergence will be best. I have converged a few Panasonic TVs and a Mits and it's a bit of work, but it pays off nicely in a much better image.
2) Focus like convergence, relies on precise alignment of the RGB guns. There are 2 ways to address that" electrostatic focus and also mechanical focus. The rewards can be slight or staggering depending on how bad the set was already. Doing both usually takes no less than 15 minutes and is fairly easy, assuming you don't ham fist it and bump the RGB screen potentiometers which makes the job take much longer.
As for a service tech doing this, well, if it's Best Buy then beware. Kinda like having a lawnmower repairman do a tuneup on your BMW. he has the knowledge, but probably won't give it the love it deserves and potentially can do more damage than good. I know a lot of folks who have had Sears / Best Buy "technicians" come out and do a lot of damage due to lack of knowledge - they often can't even enter the service menu, and sometimes are totally clueless.
Drop me an email at jason_flynn@yahooSPAM.com
(remove "SPAM" from my email address first) and I'll be happy to come over and help out for free. Hey, I actually enjoy this kinda stuff. ;) Alternately, you can have a BB tech come out but that's a mixed bag. Preferably, you can hire a local "ISF technician" (Steve Martin is a local expert, not the comedian just same name) who can do wonders, but it'll cost maybe $500 or so. I can do everything the ISF can do except for a greyscale calibration, and I can even do greyscale fairly well without the equipment by eye if you want.
Long story short: these things are sensitive and don't like to be moved. You gotta get under the hood to tweak her back up to snuff, and you may well find that we can get it looking MUCH better than when it did new.