The tiny amount of helium that they use wouldn't lighten the jockey by any more than a few ounces at most - it's about the same amount used to fill three helium balloons, which can be held down with a very small bag of sand.
A row of terraced houses in London (or anywhere for that matter) would never - even in Victorian times or even earlier - have been constructed the way it is depicted (with the walls in the loft/roof space only going halfway up, so that Dylan and Jed are able to clamber between the lofts of the houses as shown). Not only is this a major fire risk (since a fire in one house would easily be able to spread to the next), there would be significant heat loss. It would also mean constructing the houses in a counter-intuitive way as it would make the roof construction much more complicated.
In the first shot of Dylan and Jez's place, there are clocks on the walls. The clock for New York says 12 o'clock. In the next scene, the clock for Frankfurt also says 12 o'clock. In fact, all their clocks are stopped at 12 o'clock.
When Georgie stands up at the roof-top pond, she casts a shadow on the background sunrise.
Dylan says Stanley Grove is in SW19 but in fact it is in SW8.
Where Jez has shown Georgie the money cases, you can clearly see the mic as Georgie heads up the stairs and says goodbye.
For the prize coupon for Zappy Nappies, Dylan and Jez have to describe in no more than eight words why they buy Zappy Nappies. However, Jez's solution - "Weighs less than a bun, holds more than a ton" - which they decide to send in is ten words.