I think the first episode was really just about setting the scene. There were a lot of "things you'd obviously try if you knew what had happened to Sam in Life On Mars" going on, i.e. Alex answering the phone, talking to the TV, etc, and I think they did that just to stop us automatically thinking "this is crap, why doesn't she just keep watching the telly late at night in the hope of a message?" etc just to show that although it's possible, she can't control it. I agree that Alex seems a bit arrogant but then she 'knows' that the world she's found herself in isn't 'real', so perhaps she's just attacking the world - remember, Sam considered jumping to his untimely doom in the first LoM episode. Alternatively, I imagine they've just overdone 'feisty' as I'm sure I remember reading somebody saying Alex was meant to be a different type of personality clash with Gene than Sam was - a bit more up-front like Gene, rather than the way that Sam was practically the opposite of Gene's methods.
As for the setting, I'm finding that the Ashes To Ashes period is getting more "wow, my dad had one of those", "wow, I remember them!" moments from me than LoM did, purely through being born in the eighties. Anyone else finding this?