This is where you need to do your research as the answer to the above is "Not necessarily".
Just getting a full 1080p 24 tv won't guarantee no judder or motion issues, this is why all the big firms are striving to develop better and better screens that can deal with motion issues better than their competitors. Sony has gone to 200hz, panasonic has gone for their neo engine etc.
Tbh if your tv is not HD and you only bought it new 2 years ago I wouldn't be going back to that retailer again as he's sold you something with a very limited shelf life.
I have just gone through the process of buying a new full HD tv so I'll tell you in a short time what I discovered over the months I was researching and testing.
I thought that by throwing £1200 at a HD TV would give me a perfect TV and I would be happy, truth is, this is not the case as screen performance can vary considerably.
I had put off going to HD for a long time as basically the digital TV technology is not as good as all that tbh, yes it is the future but the problem is we're in a position where we don't yet have all the ingredients in place at the moment for it all to work as smoothly as the old CRT and analogue broadcasts system gave us for years. The digital signal we currently receive in our homes is not 1080/24 and only the very best screens can deal with motion etc without any noticeable flaws and so to move to digital technology and HD at the moment we have to accept compromise. Also remember that because some of the digital channels are sending us a picture that is so poor it makes a very good HD TV look terrible but that is down to the signal, on any HD tv the information on the screen is only as good as the information being sent to it.
My problem was that £1200 was a huge amount of money for me to spend and was going to have to be financed in some way to justify the outlay. So I was hoping that technology had moved on enough to mean that I would get that "perfect" TV performance for my £1200 and it hasn't, I'd get good, but not perfect.
Me being me and the fact that I would have to make sacrifices to shell out even £1200, to sit there and get motion blurs and other issues, even now and then would have me sat there quietly burning up inside with dissatisfaction.
So back to the point, this technology is moving on very very quickly and in 5 years time there may well be that "Holy Grail" of the perfect TV for a reasonable outlay so you may wish to wait and see if you can cope with the issues you have with your current TV.
If you must or can afford to change your TV then currently there is only one range of TV's that people will happily say "You won't be disappointed with guaranteed" and that is the Pioneer Kuro Plasma's, at £2000 for the smaller 50" screen (if you shop around) I simply could not afford to do it but maybe you can. Be quick however as these TV's are for some reason not going to be made anymore and are becoming hard to come by, I was told Pioneer was bizarrely withdrawing from the market for some reason.
What I did was get myself a full HD tv that was at a stupidly bargain price (£549 with a five year warranty) and although some might say it's not the best, I know it's not but it's pretty bloody good and pretty much as good as most things out there below Kuro standards and the fact that it cost so little means I can sit watching it very happy knowing I can still afford to eat and I got great value.
In 5 years time, if the technology is better and Kuro type quality is available at half the price then I will take the big money plunge, til then I'll be happy
Hope I've not bored you silly but I just thought my recent experience and learning curve from relative novice to the current tv market to making what I think was the right decision for me, might be of some value to you.
Take care and good luck, Lee