Baby Albert is wearing a blue babygrow when he's carried across the yard by Harold. He's not wearing it when Harold enters the house with him, and he hasn't got it on when he's discovered in the barn by Albert and Harold in the first place.
The morning after the night out seeing the stripper, after Albert has slept in the stable, as he picks up the milk on the doorstep he has rough facial hair. When he takes the milk into the house he is clean shaven.
At the end of the film, when Harold and Albert get beeped at and overtaken by Prince Philip's Rolls-Royce, they are going down Great George Street, with Big Ben a short distance behind them. But in the next shot, with the Rolls-Royce still just in front of them as if only a few seconds have passed, they are suddenly on the Mall approaching Buckingham Palace, about a mile away.