First off, to the original post, I would be of the opinion that PD's read zillions of LORs and if YOU read it, and believe it lacks something (assuming you don't read a lot of LORs), then it probably is lacking.
That being said, if you think that it may be broad, that is not nec. a bad thing. It would be nice if there were specifics in there, but if it accurately (or overtly positively) characterizes you, that should be good enough (IMHO). Ideally, you want a letter that really illustrates (as you said) you as a person so the person reading it says something like, "Man, I think the pope outta take a bullet for this guy!" but I don't think that happens too often 🙂 I would guess that most LORs are like you described and are pretty positive and bland, but I was told once that there are certain keywords to look for in LORs that this is not necessarily the person to hire - ie. enthusiastic, or hard working w/o any mention of knowledge base, etc. and someone who reads these things all the time should be able to pick up on them.
hope this helps