I've just started playing Skyrim. 

I've got to riverwood and been told to go to the Jarl at Whiterun. When I get to the locked gate there is no guard to let me in. I have looked online and this seems to be the only way in. 

I managed to get into the Jarls building by getting put in jail. So I've now spoken to the Jarl and got the next quest; to retrieve the dragonclaw. So I leave the building to enter whiterun. But Whiterun is just one big glitch. There is no ground and you just fall to your death. All you can see are the doors to non-existant buildings. 

I manage to fast travel to Riverwood. So I set off to find the dragonclaw up around black peak borrows (or something) but I encounter the same problem there. The terrian just stops and the trees infront of me are just floating in the air and I can go no further. 

The absent guard at Whiterun gate seems to be a common problem but I can't find anything about the massive glitches online. Has anyone encountered this? What should I do? Have I got a faulty disc, and should I send it back? Thanks.

I had similar problems at the start of my playthrough, but i just started a new game. You dont seem to be to far into it, so try starting a new game and if the same thing happens then take it back to where you got it.

Yeah, I started another playthrough but had the same problems.

Did you install the latest update? The first three updates fix a lot of bugs. The newest patch just adds 4GB RAM support.
On which platform are you playing? PS3 is generally more buggy
If you play on PC, do you have any mods or retexures installed? Although I never had bug associated with mods, this could also be a reason.

Too bad. You should've known not to buy this game for the PS3.

I guess that un-installing and re-installing the game data would fix the problem. Never heard of a disc which problems such at those, either it run or it doesnt run.

Funny fix i found out about by accident.
Didn't have this problem at all, but if you get arrested by a Whiterun guard outside of whiterun, they'll take you inside to confiscate any stolen goods or to serve time.
That way you bypass the whole "Guard unlocking the door" action, and start of right in front of Dragonsreach.

And the main gate remains unlocked as well, so that's a plus.

It's Skyrim. It's a feature, not a bug.

Delete all of your data and try again... Sorry...

Try it with out any updates. Past that point, then do the updates.

Damn, the only problems I've had the PS3 version is when you cannot take the dragonstone from the Draugr Overlord (after you kill him) until you leave the room and then re-enter it.