This is a great anime series that many will love. It is not, as the title suggests, the complete series however. This is just series 1, with series 2 being a separate release on a later date. With that clarified though, we should get down to the meat and potatoes of the set (though I'll aim not to spoil the actual plot details; that is what Wikipedia is for).
Be forewarned now; if you are not a fan of perversion, or the associated humour that goes with it, you will not enjoy this series. It has a great storyline that really starts to build up with Nymph's arrival in episode 5, but no storyline in the world will make up for the amount of perversion that is present if you dislike that sort of thing. There is no actual nudity (anytime it comes close angel wings conveniently cover the screen), but every episode has more than its fair share of panty and bra shots, as well as some strong language in some parts. I happened to quite enjoy the way that humour was incorporated into this series.
This set has all thirteen episodes from the first season, plus a bonus fourteenth episode that was released - but not broadcast - in Japan as an OVA. All fourteen episodes are split across 2 Blu-Ray discs (8 on disc 1, 6 on disc 2). They are also included on 2 DVDs (which curiously is split slightly differently, with 7 episodes on each disc). A third 'Extras' DVD contains the usual fare for an anime release; that is to say, trailers for other recent/upcoming dubs, and textless opening/closings. The closings are the real gem of the extras. Unlike most series, which have just one or two different endings over the course of the series, every episode has a different ending theme. This actually warrants the extras having their own disc rather than shoehorning them onto the other DVDs, a smart decision by Funimation. Curiously, though, these Extras are missing on the Blu-Ray set. The dub is well acted, and all of the voice actors are well chosen. The voice for Tomoki surprised me at first, but I got used to after the first five minutes; and honestly, I found that it actually fit the character quite well.
In summation, this is a fine series. It well animated, well voiced, and very nicely presented. If you aren't a fan of perverse humour this may be a release you want to avoid, but I heartily recommend Heaven's Lost Property to all others. It may just be the best series I have ever picked up.