It would be easy to point out the places where I would have done things differently, but first let's see what van Pelt aims to do and if he succeeds:
This grammar was not written for Aramaic scholars or for students interested in comparative Semitic grammar. Rather, the purpose and design of this grammar is to provide the average student with a working knowledge of the Aramaic language appearing in the Old Testament. It was written for those students who desire to study, teach, and preach faithfully from those portions of the Bible that appear in Aramaic. (page x)
I kept reminding myself of this paragraph as I read through the grammar. It is not fair to evaluate a textbook on the basis of what I would have done; I'm far more interested in comparative Semitics and historical grammar than the average student :)
As far as layout, the book is 8.5 x 11 inches and the text is large enough that even my eyes could easily read it. The tables are well laid out and clear. The use of footnotes for interesting, but not essential, information is good, allowing the interested student to obtain more background.
The book assumes the knowledge of biblical Hebrew; there are repeated comparisons to how biblical Aramaic is/is not like Hebrew. Here is where I would have brought in some comparative Semitics and historical grammar to explain the ש/ת interchange, as well as other consonantal differences. He does mention the Canaanite shift, which is good. But, again, I reminded myself of his purpose paragraph. The average student would probably be more confused than helped.
He begins with the nominal system, including particles, conjunctions, and prepositions, and then proceeds to present the verbal system, beginning with the Peal and then giving the derived stems. There is a great deal of emphasis and explanation of weak verbs, which is very helpful when you consider that the majority of the verbs in biblical Aramaic are weak.
The grammar section ends with paradigm charts before launching into the reading section. The book includes all the Aramaic sections of the Hebrew Bible, complete with extensive annotations. The annotations include things like identifying a difficult to figure out root, metathesis, idiomatic phrases, etc. The strange thing about the reading section is that the order of pages is English, not Aramaic. You start reading on the left hand page, then proceed to the right, and turn the page as if it were English. I'm not sure what the logic of that is. I would think that the page order would be Aramaic, but that is a minor quibble.
The book concludes with a dictionary, based on HALOT, with one-two word glosses. Adequate for reading the passages, but for more extensive background, HALOT or BDB should be consulted.
What do I think of the book? As one who learned biblical Aramaic via the “here's a text, lexicon, and Rosenthal, now read it!” method, this book is a vast improvement. I suspect a highly motivated individual could teach themselves Aramaic using it—as long as they already know Hebrew. The explanations are clear enough and the notes in the reading will keep you from getting discouraged.
In answer to the opening question, did he succeed in doing what he set out to do? I would answer, "Yes, he did." As I mentioned, the layout is attractive and the explanations are good. As anyone who has ever taught a language will tell you, there is no perfect first year grammar for any language—except the one you write yourself! If I were to teach biblical Aramaic, I would probably adopt this book, but assign background readings in Rosenthal's A Grammar of Biblical Aramaic. Of course, if someone were to create an immersion course in Aramaic, that would be best!