Not being a super star on the ball is not a weakness. The fact that he is composed and picks out simple and efficient passes is all he needs to do! He's not technically gifted, but his technical ability is not in doubt. It's definitely not a weakness. If he was a forward, winger, or offensive midfielder then yes, it would be a weakness. But he's not; so it's not. You don't sign for Manchester United if you're not technically adept.
I'll argue with you on the terrier front too - Hargreaves never EVER shirks a tackle, yet he's not what you would describe as tenacious. Again, I'll compare with Makalele; he wasn't a terrier but he knew where and when to be to break up play. Hargreaves is similar.
And for the record, I never said Hargreaves was a complete player - I merely stated he has no real flaws. I'd like to point out that distinction.
He has his strengths, sure, but every single 'basic' skill or attribute that a professional footballer requires, he possesses: he can kick a ball cleanly, he has a decent touch and control, he can win the ball in the air, he can pass, he has good stamina, he's not slow, he has a footballing brain, he works for the team, he can tackle. To me, that spells pretty much flawless.