Well I think we need to be clear what explain means. With the assumption the field changes on observation then the double slit is explained. Did you expect the explanation not to assume some things? Any explanation does that.
It doesn't explain the measurement 'problem' (postulate is probably a better description than problem - but its pretty standard so I will stick with it) which any observation in QM has - but in general QM merely accepts it as a primitive of the theory.
In modern times decoherence is used to elucidate better the measurement postulate which has a number of parts. It explains a number of those parts such as a preferred basis - it doesn't explain the so called problem of outcomes which colloquially is why do we get any outcomes at all, or more technically how an improper mixed state becomes a proper one. Exactly what that issue is, is explained here (sorry that its rather technical but we are getting into deep waters here):
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf
If I remember correctly that book you got also mentions decoherence - but doesn't give any details. This may help at your level:
http://www.ipod.org.uk/reality/reality_decoherence.asp
Thanks
Bill