I was just at Bestbuy watching my boss hit walls in the GT5 demo and I noticed that all the shadows were perfect.  It was on their Sony Bravia tv that they are advertising right now, running on the PS3 slim.  It led be to think 2 things.
 
Is it just my old LCD TV and old 60 gig backwards compatible PS3 causing the shadows?
 
Or was it just simply that the demo's shadows are fine.

The shadows are worst when you play in the Day/Night Cycle tracks, it has to do with the sun's placement and some other crap.   
 
I don't know if Sony TV's are better with them, or if it's a placebo.  But I do know that the absolute worst shadows are with the time cycling.

My boss was playing the demo on a rally dirt track, and it went from day to night in seconds.......looking absolutely fantastic.  I'm not just saying that to stress a point, it did happen lol.  
 
It was probably just the demo, but maybe it is the TV?  My tv is a 5 yr old 720p 40 inch samsung, that tends to stretch images really bad.
 
This is basically what I saw.  Except with rally racing and day/night cycle.
And it was posted back in September
 http://www.gtplanet.net/confirmed-gran-turismo-5-playable-demo-at-best-buy/

It's kind of sad that it's come to the point where people have to write "Not Trolling" because people scream troll at the first thing they disagree with. Just an observation.

From a technical standpoint, a tv should have no impact on the 'jaggyness' of shadows. Shadows are created by rendering a shadow map, which is usually a grayscale image (at a specific resolution, say 256x256). Once the shadow map is rendered, the main game scene is rendered, and for every pixel in the main game scene, the playstation checks the shadowmap to see if that pixel is in light or dark. The jagginess is the result of a low resolution shadow map, you are literally seeing the 'pixels' of the shadow map being casted onto the main scene. So to remove jagginess, there a bunch of techniques, the easiest one being to increase the shadow map resolution, but various things like processing time and memory requirements means they have to keep these things very small. 
 
Long answer to a short question, but its completely to do with how much memory a given track takes up (hence there being more memory available for shadow maps) or how complex the graphics in the scene are, thus allowing more time for shadow map filtering (also remove jaggies) 
 
you can read a much more full explanation here: 
http://en.wikipedia.org/wiki/Shadow_mapping

Not that I care, but the shadows definitely can get pretty jaggy. The thing I don't like is that sometimes they do a weird flicker like they are not solid.

yes...sometimes they are jaggy and sometimes they arent.  I play with the interior view and the shadows look fine majority of the time.  I notice in replays that the cars have some jaggy shadows from time to time but when they are in motion it kind of blurs it so you don't notice.  All reviews I read just say the shadows are horrible and jaggy and don't mention that that only happens on occasion.  This is the full game I'm talking about...not a demo.

It also happens with smoke and dust as well. You can see it at the end of this video: http://www.justin.tv/monkeydluffy11/b/275300942

" I was just at Bestbuy watching my boss hit walls in the GT5 demo and I noticed that all the shadows were perfect.  It was on their Sony Bravia tv that they are advertising right now, running on the PS3 slim.  It led be to think 2 things.  Is it just my old LCD TV and old 60 gig backwards compatible PS3 causing the shadows?  Or was it just simply that the demo's shadows are fine. "

You're still early in the game and the demo station had all the premium shit turned on. 
 
Just a guess. I honestly haven't tried it yet.

You need to get to level 30 to unlock good shadows.

Everything I've read about the game screams "rush-job". Graphical glitches, poor quality, the majority of cars lacking polish and so on. Worrying that the development cycle was so long.
 
I'm not a fan of racing games, on the whole, though.

The shadows are pretty terrible on my TV too. In fact, on Cote d'Azure, when you go into the underpass it literally looks like the shadows are crosshatched. It looks absolutely terrible.  

" @GetEveryone:  I wouldn't say they rushed it, I think they just committed to way too much content got it all in, and didn't have enough time for the foundation.  To be honest I would've been happy with 200-300 premium cars and no standard cars at all.  Watching a video its hard to say graphically its impressive, but go to the photo thread....... some of those in game photos seriously look 100% real.  PD put so much detail in each of the premium cars its friggin scary, but when their in motion, not so much.    Guess it depends on the perspective. "