One of the first characters introduced in Scrapped Princess is Leo, a naive, incompetent knight wannabe. He's annoying right away, but mercifully his role diminishes after a few episodes. The action picks up, the sci-fi world details become intriguing, and things start to look up. Based on the other reviews here, I figured that I'd made it through the "slow start" and could settle back to enjoy the show.
Unfortunately, as the series progresses, Leo returns to prominence, and two other main characters sink to his level. Shannon, the princess's brother, takes willfully stupid and rash actions, at odds with his "protector" character archetype. The princess herself is revealed as a spoiled brat obsessed with baths, clothes, and perfectly cooked eggs, who won't fight and won't even expend any effort trying to understand the role she's been given. It becomes impossible to root for her because she doesn't even try.
If you watch the first couple of episodes and find Leo tolerable or even charming, then you'll probably enjoy the series. If you hate his guts like I did, save your time and move on, because you'll probably end up hating everybody else, too.