It's harmless, but it's also tonally inconsistent nonsense.
The source material is a PC Eroge Visual Novel from 2008, i.e. computer "choose your own adventure" porn. The hero is Teppei Arima and there are four heroines you can, um, woo. (They can even get pregnant.)
This, on the other hand, is a TV adaptation. Twelve episodes is hopelessly inadequate for a Visual Novel, so they've simply chosen one of the four girls and are telling her story. (Apparently some fans were unhappy because they wanted a harem show and more romance with all four brides. These people can sod off. Ditching the harem angle was the best decision this TV series made, although it's only half-ditched since they'll all end up worshipping Teppei's shining wonderfulness anyway.)
It starts dramatically. Teppei is the son of poor but hard-working parents. We see their silly daily banter as Teppei heads off to school... and that's the last time he saw them alive. Someone murdered them. That was shocking.
After that, Teppei gets adopted by his own grandfather as heir to the Arima Group, an industrial conglomerate with more money than most countries. (Teppei never knew about this.) Grandad gives him a spare mansion to live in, for instance, with 65 maids assigned to wait on him. He then gets sent to a school for the stupidly, insanely, cartoonishly super-rich, where he fits in worse than a ten kilo suppository. Yes, the show's already started getting silly. He meets the girls. This is actually well done, since Teppei is both a startling and startled new element in their world. The relationships and challenges feel plausible. I quite liked this phase of the show.
At this stage, the show's light-heartedness is funny.
Things then get even sillier. The show decides that it needs villains and action sequences. We learn that the Arima Group hasn't heard of data backups, that a sword can knock aside bullets and that you won't get hurt if you jump from a bridge on to a speeding train. There are DNA-based computer viruses, as per the 2007 Transformers film by Michael Bay. Heroes using swords to attack their enemies will only harmlessly knock them out. If you'd been waiting for payoff for the murdered parents... well, sorry. There is eventually a link, but by then the show's degenerated into good-natured but inane action candyfloss and it's almost annoying to have the show's serious beginnings tied to this absurd finale.
(That's one of the show's two annoying episodes. The other's ep.6 and its "peep at girls in the hot spring" storyline, which has jokes that might seem funny if you find it amusing to watch boys being offensive and stupid in a situation where the consequences of being caught could easily be terrible.)
There's also bold fanservice. The anime doesn't go as far as the visual novel (although there's a 2010 anime OVA that does), but it does have blatant panty shots, mega-cleavage, transparent nightdresses, erection jokes, rampant nudity and nipples. The winning girl is so happy in ep.12 that she says hello to Teppei's penis (offscreen). (Literally. She greets it.)
Who are these girls?
CHARLOTTE HAZELRINK (pale pink hair). Has a gloriously badass elderly butler called Alfred who can do Mad Max action sequences. She's the only actual princess (of a country called Hazelrink), but not stuck up at all. Instead she's irrepressibly cheerful and forgiving, which gives her easily the best, most natural chemistry with Teppei. She's also either slightly flirty or completely oblivious to dirty stuff. (Watch her carefully in ep.8 though and you'll see that she's putting up a deliberately cheerful front.)
SYLVIE VAN HOSSEN (yellow hair). Proud, dignified and seemingly incapable of relaxing or letting her hair down. She's a noble of an East European country and her hobby is fencing. Both she and Teppei are surprised to learn that she's Teppei's arranged fiancee... but the show's surprisingly sensible about this. Teppei immediately checks to see if he's allowed to say "no" (he is) and they agree to treat their engagement as a provisional agreement that means nothing to them until they've accepted it.
SEIKA HOUJOUIN (dark brown hair). Polite, nice and generous until she learns who Teppei is, whereupon she becomes his enemy. She's for all the tsundere fans, in other words. She hates the Arima Group. She's also the only girl with normal-sized breasts (so she gets more panty shots instead).
YUU FUJIKURA (blue/black hair) - Teppei's maid. She's really conscientious and nice, but she has an exaggerated sense of her inferior social position. As far as I was concerned, who to cheer for was a toss-up between her and Charlotte. They're the two who get on best with Teppei, with Yuu being his ally in this world of loons. They understand each other, whereas everyone else is an alien from Planet Moneybags.
I enjoyed a lot of this show, but I couldn't recommend it. Its genre will turn off many people, with its fanservice and its escalating Teppei-worship. Its last few episodes will turn off others, as the show becomes a silly, lightweight, badly paced action movie that's not even taking itself seriously. However it's possible to defend the good episodes. They've got a good sense of humour. The characters work. The harem nonsense is nearly plausible. Even the fanservice is light-hearted and amusing, not nasty. (I also agree with the anime's choice of winning girl.)
If you're thinking of watching some anime, though, there are thousands of better shows than this.