If you're thinking of taking a shot at this anime, I strongly advise you to click that little red X on the top of your screen and don't look back. I'm sure you can find other ways to use 60 minutes of your life.
If you've already watched it, however, there's not much I can do. Go somewhere quiet and lie down. Take a nap. You'll probably develop a headache from trying to make sense of what you saw. When you've rested, get yourself a lawyer. You'll want to get your time back from the creators of the show.
*Here Be Spoilers. But then again, there's not much of a plot to spoil*
Storyline? What storyline? Saishuu switches from Slice-of-Life speed to Action about 3/4 of the way into the series. Of course, with 5 minute episodes, there are time constraints, but the contrast in speed (and apparent plotline) is beyond horrible. It feels like the series only had the first episode and the last episode made from the storyboard, and then cut the 2 into 12 five-minute episodes. You'll notice the HUGE gaping plothole near the middle, and will probably fall in.
Character designs were alright. Nothing amazing quality-wise, and none of it moved (Saishuu's world apparently does not have wind). The colors, however, were soft and calming, which is nice if you're into this style.
5-min Episodes = no BGM. There's rarely any soundtrack, and when there is, it doesn't match up with what's going on sometimes. However, Eufonius sings the ED, which is probably the best thing that happened to this series.
The voices were not matched well either. The main boy has a very feminine voice even though his character isn't girly at all. Also, most of the voices (if not all) carry zero emotion.
No character development whatsoever. The first few episodes were slow, and characters were introduced. Then most of them magically disappeared by about the 8th episode, and never came back. Odd? You bet!
If you can manage to ignore all the outrageousness and plotholes, Saishuu can actually be enjoyed in an awkward way.There were some (rare) moments of genius as well. The flying bit was cute, and the beach episode was so cliché it was funny. Other than the complete lack of emotional scenes, it could be enjoyed if forced. And of course, the Transformer-Whale-UFO is all worth it in the end.
If you turn a blind eye to all the weak spots, you'll have your eyes closed for the whole duration of the anime itself, and only watch the ending theme.
With that said, Don't Watch! If you love your life, find something better for your time :)