I kind of knew something like this would happen.. Basically, I started the Bedlam Job from Delvin @ Thieve's guild and I have definitely stolen over 500 gold yet there is no notification/quest continued.

The objective is to steal 500 gold worth of items from Whiterun without being spotted on any items, I have done this and even stole an Elven Warhammer around 565 gold on top of my overall stolen items.

Please help! I need to get past this.. FML bethesda have released a game during development to us PS3 players.

Are you sure you actually stole it? Sometimes items are just available around town to take and won't count as stolen. Also make sure your journal didn't update anyway even if you didn't get an on-screen prompt. If all else fails, all you need to do is go back to Delvin and tell him you don't want to do the job. This will cancel the quest and allow you to either restart it or pick a new quest.

For the moment, put what you stole back. Go back to Devlin and cancel the job. Then engage Devlin again and ask for another Bedlam job. Perform the job and see if the same bug raises its little head. One occurrence does not mean you have a "bug". It could be a momentary problem because something failed to initialize properly.

Try to stick to Dragonsreach when lifting things. Just walk around Farengar Secret-Fire's area and lift his magic items. Then proceed to the Jarl's quarters and work your way through there. The game sometimes doesn't want to recognize people's homes as places that count. I've noticed that if you just stick to the Jarl's places, you can beat these missions pretty easily.

The easiest way to beat the bedlam jobs is to also take a sweep job in the same city. The unique items in the sweep job count towards your total for the bedlam job, so you end up completing both by doing one.

The elven warhammer was in an expert level display case in the Jorrvaskr living quarters.
thanks for your help guys, I will try these methods now.

I believe stealth is broken for some folks in 1.3 and what may have happened was same for me, you weren't truly "hidden" and thus, the items don't count towards your score. (Remember when Delvin says "It only counts if you aren't seen."?)