My only gripe with him killing Alton was that it was gratuitous and unnecessary, like MikeL said. He didn't need to kill Alton to escape, and that's why I don't like that scene. If he told him to feign death it would work the same way.
But that's kind of a biggie, isn't it? It turns a character from cruel guy ready to do anything to get home to crazy sociopath. I actually do believe that if it was a sure way to get back to Cersei, Jaime would kill his relative without much worry. But killing him when it's absolutely unnecessary is something that Ramsey Bolton would do. (not even mentioning that book Jaime would like Alton as shown here, just as he liked Loras). Not even Roose, because it's also STUPID - if Alton played-dead, they could overpower Karstark and guards together so much easier! So he not just killed a relative, but killed him for shits and giggles and counterproductive to his directive.
Many people pointed out problems with this scene, like stupidity of Karstark guarding Jaime by himself. But what exactly was Jaime's plan here?
1. Kill relative.
Why would Karstark enter the cage after Jaime just violently attacked a prisoner? Why would he do it alone? What did he think was going to happen? Isn't Jaime in the middle of a camp? (He has to be, right? Or is Robb criminally stupid too?) What Jaime did after getting the key, isn't he surrounded by enemies? Including sentries. What exactly happened, did he kill sentries? Did he get a horse? What? You can't show escape plan and not show a difficult part of it. Why would he assume that Karstark is going to wander into his cell? I literally don't get Karstark's thought process here, why wouldn't he call people? He deserves some kind of Darwin award for sure. Why not ask Alton to pretend to be unconscious so they could, you know, together overpower the guards? Did Jaime just want to kill this likable guy for no reason whatsoever?