If the government thinks Zeta is a killer terrorist robot, why haven't they frozen his credit card?
It might be a card that hacks the credit card computers locally, so it can remain untraceable and always available in case a connection to the Government accounts cannot be made for whatever reason.
Cred cards =/= credit cards. They're more like universal gift cards—they contain certain amounts, are disposed of when they run out, and aren't linked to bank accounts or stuff like that. Basically, Zeta's card hacks the system so it never registers as empty. There's no actual money behind it. Theoretically, if he and Ro used it on a big enough scale, it would destroy the economy.
What's with Zeta's head? In the Batman Beyond episode that introduced Zeta, his head looked a lot less human. Now, from a real-world standpoint, the change makes sense — the head he has in this series can show facial expressions and makes him look a lot more sympathetic. But in-universe, what happened? Whatever it was, it stuck — in Zeta's other appearance in Batman Beyond, he looks like he does in this series, and nobody comments on the change.
In episode 3, Zeta is being controlled by some brat twelve year old kid with a universal remote. Ro is right next to the kid, watching him control Zeta with this remote, sees the kid sic Zeta on someone, and runs after Zeta to stop him — why the HELL couldn't she just take the remote away from the kid? He's friggin' twelve! Grab it from him! But no, she has to go program another remote to battle with the kid over control of Zeta, then...get Zeta to destroy the first remote.
Well, remember that she had no idea how the thing worked, and one accidental press of the wrong button could easily make Zee explode or be rendered inert or something equally unpleasent, and even destroying it might have catastrophic results. There were other options, certainly, and doing what she did was probably not the best one, but just grabbing a device that you have no idea what it coud potentially do and that is linked up to your only friend probably isn't the greastest idea in the world.
Zeta is a government created infiltration unit with the ability to holomorph into anyone. So why in every appearance does he take the same appearance? I know its supposed to be his default form and everything and its to help the viewers know that its Zeta but he's a wanted fugitive and he always appears the same when hes in a public place. Several times in the show you see his default form is on wanted posters and everything. So why dose not he just change his apperance more often to avoid being found. I mean I would understand if he took that apperance when its just him and Ro but it really makes no sense when you really think about it.
It doesn't matter anyway, as being seen next to Ro would alert the agents that it's Zeta. Also, changing forms constantly means that Ro might not remember what Zeta looks like that day, so she could easily miss him if they split up and had to meet again. If Ro is going to be recognized, might as well choose a form that Ro is familiar with and could easily pick out as well.
He's forming an identity of his own, including his own beliefs, ideals, morals, sense of repulsion and social skills. It's not a stretch to say he's also developing his own identity in that he wants an appearance of his own, his own physical visage. He appears as he does because it's part of him becoming his own person, the same way the rest of us dictate our own appearances.