This is a very useable resource. From a pragmatic perspective, if it works, don't fix it. I agree it is difficult to deal with romanized script at first, but I'm leaning it.
If you are going to to spend time in Iraq or working with the dialect, this book fills a gap left between Hans Wehr and other MSA materials, and the basic Iraqi phrasebooks which are so easy to find. Highly recommended for all professionals in this field. The written examples included for each definition are particularly helpful, and give one a feel for how dialogue is structured in Iraq.

As much as I like to see words in the orginal script, you are unfortunately at a loss if you do not already know the basics of the dialect when you see the words written in Arabic script. As others have noted, probably the best way for dialect to be represented is either by a set of roman letters or by an internationally accepted script based on Arabic. Since the latter is a bit advanced for most non-native Arabic or Farsi speakers, the system in this book is the best alternative.

To illustrate, take the basic word for "coffee," a simple, universal concept in the Middle East.
In MSA, it's Qahwa
In Hijazi and other Gulf dialects, it's Gahwa
In Syria and Lebanon, it's 'Ahwa.
But in arabic script, they are all spelled the same.

If not for the romanized pronunciations, how would you know, unless you already had experience with those dialects?

Well, I have spent a year in Iraq and will soon spend another, so I look forward to putting this resource to good use.

I agree with another reviewer...it's more helpful to have everything written in Arabic. And, while the dialect is technically not a written language, there are ways to write it...modifications that have been made to aid in the pronounciation of the dialect while still using Arabic letters. That would be MUCH better.