I watched them back-to-back on DVR last night.
I felt some of the acting was laid a little thick in places, like in the first episode when Barry gripes at Dr. Wells and then goes to confide in Arrow. Barry was reacting to the death of a bystander which triggered memories of his mother's death. That's fine, but it fell short of being "earned".
Another slight problem is that the pacing in the first episode had super speed. It just moves too damn fast, and I had a hard time connecting with any of the characters without making a conscious effort.
The second episode was a step up from the first, because of the family angle. I felt bad for Joe whenever his adoptive son disrespected him. The realism made those scenes awkward to watch (but I was glued). Their reconciliation at the end was heartwarming.
Barry's storyline was handled better in the second episode. He's enthusiastic to use his new powers, he suffers a humiliating defeat and flees, his confidence is damaged, etc. I think we'll see this happen many more times.
The action scenes are exciting, the acting is professional... I look forward to episode three.