Offensive: Resisted by 2 types (average). 1 type is immune. Not SE against any type.
Defensive: Weak to one type, NO resistances. And as another user mentioned, being neutrally affected by a lot of types really doesn't help that much (See Sableye, Spirtomb). Also Blissey is the ONLY Normal type pokemon in OU, and that's only because of it's ridiculous defensive stats.
At least Ice types get STAB on one of the two best special attacking types. Normal types have NO positives. And this is coming from a guy who really likes Normal types.
Not changing this sig until we get a new main series Tales game released on a Nintendo console in the US Dictator of the Zelda Wii U Board