Abby's special toy is frequently washed and never smells of her. Maybe one of the twins was sick on it and that was why it was washed? Any number of reasons could mean it had to be washed.
As for the fridge, you are in a rental property in a hot country and the fridge breaks. The landlord is refusing to fix it or taking a long time to do anything about it, you've enough cash, you go out and buy one. Bloody sure I would. For all we know the landlord said to him "you go buy one and we'll forget your rent this month"
With the cadaver dogs, I'm not sure why them pointing out the evidence is flawed means they were dismissing anything, I think the point of dismissing it was so that people keep looking for their daughter. They've said on several occasions that they want people to keep looking for her and if people think she is dead they won't do that. I'd be more likely to take the view that as doctors they are scientific people. So on the evidence being presented to them they would first of all look at the quality of the evidence and then work out whether it is worth following up. And the fact is that all across the world, Cadaver dog evidence is not considered, by itself, to be reliable. It is used to give detectives an indication for further investigation. With the amount of supposed DNA evidence of blood and death that was all over the place, the clean up operation would take quite a while and the timelines already made public make it quite unlikely they killed her. Don't forget cadaver dogs apparently indicated that Shannon Matthews had died in her home. Thank god people didn't stop looking or maybe she wouldn't have been found when she was.
I don't buy conspiracy theories of "friends in high places" Powerful people don't just protect two random members of the public, there has to be a quid pro quo. People talk of links with the Murdochs and how that has been a huge advantage to them, but the Murdochs are not untouchable so I'm not sure why any supposed friendship would be of benefit. Not only that, look at what the Murdoch press did to them, hacking their phones, publishing her diary, and they were really scathing about the press at the Leveson report, calling for stricter regulation and have been very outspoken about it since. Does that sound like someone Murdoch would be going above and beyond to protect?