1) Irreversibility, ie if someone sends to an incorrect / dead address / loses keys then its gone. Or people injection malicious stuff into the blockchain leaving it there forever.
2) Theoretical anonymity. While we all like privacy, there is a problem when something goes from 99.99% untraceable to 100% untraceable (TOR based tumbling). There ARE cases were its important that criminals are traceable even with great efforts, else it makes Bitcoin users a target. Imagine how attractive users are when the goods they take are untraceable, unmarked 'bills' with no risk of ever getting caught. I don't like it.
3) Vulnerable to attacks. With no central body that can react quickly, things like transaction floods can temporarily damage the network. Because it takes a community effort or dev census to nullify the attack, its much slower than someone who can implement needed changes instantaneously. Ie Theymos pulling the plug on the servers when he noticed the intrusion.
I would argue that each of these is a feature, not a point for criticism
1. Irreversibility is a feature. You can safely ship a good, knowing that you will be paid and not defrauded.
2. Anonymity is also a feature. Eg. My landlord doesn't know I got a raise.
3. It is a dynamic system and much more resilient to attacks because there is not a central authority to attack.