It's hard to review this one, but the standard I will use is not to treat it as part of the franchise it belongs to, but as a wholly separate entity. Story:The Tenchi Muyo OVA's are marked by having an unusually strong plotline despite being a "harem" anime. GxP however, takes a step away from that. Directed by the frequently manic Watanabe Shinichi (aka Nabeshin, aka the guy who dropped Excel Saga and Puni Puni Poemi upon an unsuspecting world) the maestro himself jumps from plot-point to plot-point with reckless abandon. While obviously having some respect for the original material, he takesliberty with the original canon when it suits him and creates the giant continuity cluster$#@! that was the 3rd OVA (and the scramble to fit it in with the original plot). The series takes a different slant from the other series in that it's got a lot more slapstick, and it's more risque in many places.
I will say that the crossover attempts and the AWFUL episode 17 (people at Funimation are going to hell for the dubbing of that episode BTW) were weak and really not necessary. The fact that this series came out before OVA 3 but referenced many parts of it, was also very disconcerting.

Art: Nothing stood out. Again, the artwork was heavily influenced by the director's style and his input is very clear.

Sound: I liked the opening credits music. But then all the Tenchi series have strong music.

Character: Enter the main character, Seina Yamada, the hopelessly cursed young man with legendary bad luck. While dropping by to see his friend Tenchi (who's also related to his best friend...don't get me started on the first of many continuity snafus) he's present for a Mihoshi-style crash landing of a Galaxy Police shuttle. The pilot, the sex object/mentor figure Amane, mistakenly things he's "in-the-know" to the wacky condition as Casa de Tenchi and hands him a recruitment brochure.
Seina then finds himself in the GP. I'm drifting into a synopsis, but work with me.
The GP, and the Jurai royals, soon discover Seina's unique ability to draw space pirates in like moths to a flame and they quickly decide to make use of that fact.
Seina is joined by the aforementioned Amane, model turned detective. His crush from back on Earth joins them as well, Kiriko. It's a mindbending rip of belief how Kiriko gets to GP HQ ahead of Seina, and if she was already aware of her royal status (yes, not even Tenchi knows that even his cousins on Earth get the royal treatment as well) what the heck she was doing on Earth before this point (reality bending, a Nabeshin special!)
Others include Ryoko Balta, who disappointingly does not share any of the roguish charm of her namesake but is also horribly miscast as a polite, almost prissy space pirate.
Then there is the child-like Neju, who true to anime stereotype, calls Seina "big brother" but is really 10,000 years old and also has designs on him.
The one standout character is the "Devil Princess of Jurai" Lady Seito. Her character is the one unique standout and plays very well in the 3rd OVA off of Washu. The other characters are quickly forgettable, but Seito will remain as one of the franchise's more memorable characters.

Enjoyment: This series was fun. It didn't wow me, it didn't make me think. It did give me headaches when they decided to screw with the established canon, but since it was continued in the 3rd OVA we have to assume that the Director and writers had some sort of blessing in this.
I recommend this to anyone who enjoys a raunchy slapstick comedy. However, this series did lack the tenderness of the rest of the franchise and will doubtlessly turn off female fans. (I know this because the series is one of my wife's favorites).

Overall: Watanabe Shinichi's unique take on the Tenchi world is refreshing and entertaining, especially after the semi-flop of Tenchi in Tokyo. It's clearly in it's own little section of the universe and is certainly a different take on things. The satire of the Galaxy Police (shown as vain and fashion obsessed) and the Jurai family (shown as a little kooky and not completely sane) is very fun given that one has seen other installments of the Tenchi franchise (namely the OVAs)