I have only got to page 57 and have not reached the point where he starts on Plato's Meno
First off it is too heavy! A text-book needs to be easily held in one hand and when it gets this big it needs to be split into two volumes.
I think someone who was beginning Greek for the first time would find the grammar explanations quite hard. In some cases they are simply misleading. On page 11 he takes about half a page to attempt to explain that while in English things have gender, in Greek it is words that have gender. Indeed he muddies the water by giving as an exception to the English gender rule that "a ship is sometimes refered to as "she" although it is not particularly female." In fact female ships are typically English in that it shows the speaker really does think that the ship is on some level female. You should never sail on a ship where the crew refers to their ship as it. If a Greek sailor were to use the neuter case in relation to their ship it would mean no more than he had in mind the word πλοιον rather than ναῦς.
His approach to nouns in that rather than teach each declension in turn he teaches each case in turn is much more logical.
The exercises are the traditional Greek to English isolated sentences. This is a method that runs the risk of throwing Greek words into a grammatical correct sentence that is however a little boring and not the kind of thing that anyone would have reason to actually say. With imagination that danger can be avoided but Beetham doesn't manage it. On the other hand, the word order does seem to me to be genuinely authentic.
He does pepper the exercises with one liners quoted from Plato and other Greek philosophers. Ripped from their context, however, I found them very obscure even after I had checked the answer key at the back. Of course this is intended for philosophy students and if they have been studying Plato they are likely to have less trouble.
And maybe the key problem for me, the reason up till now I have not looked at this book is that I don't really like Plato. Xenophon, if I were to meet him in the flesh, I am sure I would end up arguing with but I'd enjoy the argument. Plato I would find simply irritating.
If you are a fan of Plato you are likely to be much more ready to overlook the faults of this book and appreciate its strengths.