Enough time has elapsed for the major questions that pu raises to have been sorted out. Here are what I see
I pass over the existence of the word 'pu', which doesn't deserve the attention of a comment.
page 7. 'olin' used with an impersonal object ('toki pona', in fact). To be sure, the teachings of the last decade are nowhere mentioned in pu, so this may now be legitimate, but throwing over the 'x li olin e y'/ 'y le pona tawa x' distinction, after all the story of driving it home seems rather callous, unless just careless (or gross hyperbole).
page 25, the example of a transitive sentence lacks a direct object in English.
'kute' meaning both "hear" and "obey" immediaely creates the paradox of 'mi kute e mama mi. taso mi kute ala e ona' (see later similar problem with 'lukin' as "look for" and "see".)
page 34 The description of prepositions is garbled to the point that the complement is not shown as natural and so the complementless cases are not seen as derivative. Not helpful for people wrestling still with 'e'.
page 35. 'toki lon toki pona' given imprimatur (though 'kepeken' is also used later)
page 36 exercise with answer on p 64 uses 'ona' where 'ni' seems called for, but this is hard to say without context and 'ona' is regularly used without a prior noun to pick up. On the other hand, the differences between 'ona' and 'ni'' are never mentioned, let alone discussed.
page 38 'nimi mi li Apu' There is so much wrong with this sentence that I could rant a whole White Knightly page (and have). At best it is better than 'nimi mi li jan Apu', though that is only blatantly false, not generating an infinite spiral paradox. I think the that sentences beginning 'nimi x li...' should simply be banned until people learn a little grammar.
page 41 clarifies the uses of o and does away with the collapse of the vocative and imperative. but in the answer on p 65 to an exercise on page 42, the collapse is used. The o sentence optative is never considered. So the clarification ends us with the same confusion as before.
page 42. The locus classicus of inverted 'pilin pona', now enshrined and inextinguishable by mere reason. No serious attempts to extend it, however.
In passing, there is no discussion of what how one kind of word becomes another, though there are many example (quite a few given as exercises). This may be good heuristic or not, but in either case, some summaries would be handy. even if only at the end.
There is no comment about the effect of intervening modifiers on verbs, prepositions or modals, maybe because there simply is none, but it would be nice to be reassured.
pages 46-7 The expanded number system only makes matters worse by introducing new ambiguities and false precision. Either get a decent system or just insist that tpers can't count (or use telephones or find street addresses or...).
there is no mention of the lack of 'pi' with cardinals and ordinals, but at least the examples are consistent in not using it.
page 51-2 'la' is scarcely developed except in connection with 'lon' (only) at the end. The useless commas are all there and in the wrong place. (Why not some useful commas, if we have them at all?)
Nice to see the accurate 'kama lon' instead of the calque 'kama tawa' for "come to"
page 55 'kepeken toki Inli' justified
'anpa' in a new, restricted sense (SLM, I suppose) and so 'noka' in an extended sense (leaving a space unnamed). 'tawa' in the sense of "according to" doesn't seem to fit well (but what does? maybe 'lon').
In general, the adding and dropping of words (which will be largely ignored, I expect) seems not well thought out and mildly annoying, as though getting to exactly 120 words (119 and a joke) were of some significance.
To be sure, pu is 1) how one person, admittedly the creator (and long absentee) uses the languages and 2) is an introductory text from which to build a deeper understanding of what is possible in tp. But, given the space devoted to totally superfluous matter (hieroglyphs, sign language, and the like) one would think a bit more of a boost was in order.