1. How often can characters conveniently end up along the same beachside in a given town, across the span of a week? And then keep running into each other with absurd consistency? Without these handy-dandy contrivances, the plot would not move forward.
2. Every single character is a stereotype. The protagonist, Lucy, is the worst offender – she may as well be the textbook definition of "genetically-modified/robot girl." But it doesn't stop there. Apparently every other cute girl in the show has incredible super powers, but always in direct proportion to their inherently correspondingly sad personal history. The supporting cast follows the same trend... there is the well-meaning yet regretful father figure... the handsome yet naive nice guy which every single female character without fail immediately wants to fuck... the equally naive girl whose efforts to fuck the handsome yet naive nice guy are consistently thwarted by her idiocy, and her desire to keep trying not waning in the presence of said guy's greater idiocy... the gung-ho ex-special forces S.A.S. GIGN sub-terrain-ninja-commando-warlock whose expertise with weapons is exceeded only by his stupidity... and last but not least, the cute little girl who's actually a malevolent demon hellbent on murdering everyone she sees.
3. The characters with superpowers are able to use their powers to a degree of effectiveness inversely proportional to the relevance their victim has to the plot. No other explanation is given as to why the girls can't always fire on all cylinders. Through lazy writing and plot contrivances, the girls can massacre an army's worth of well-armed and trained men yet take an entire episode to deliver a blow in excess of a swift breeze to a major character.
4. The nudity is absurd. Literally within the first 10 seconds of the intro you've already seen the main character butt-naked, and within 10 minutes of the first episode, you get more of the same. Actually, this is true of nearly every episode (regarding more than just the protagonist, anyway...). Some poor fools would argue that this nudity is a manifestation of the child-like innocence or purity of the given characters whenever it is shown – however, this is so overdone by the 100th time it happens that it loses all meaning. For that matter, the central theme of innocence and discrimination is entirely conveyed through the first episode; it is pointless to watch beyond that if you're only doing it for the philosophy the fanboys (and girls!) have convinced you lies beneath the surface. And while we're at it, let's just ask ourselves if it's really such a big deal that innocence and discrimination are even being discussed – what, this is the first time you've heard of this shtick? Perhaps in anime, perhaps anywhere; in either case, go watch Grave of the Fireflies which is everything Elfen Lied wishes it was and more, yet ironically (and thankfully), in much shorter a runtime.
So basically, Elfen Lied is just a generic superpowered-kawaii-girl type thing for schoolgirl fetishists.