Having units with orders move at the end of turn isn't inherently bad, but the interface just doesn't support it - if you're going to have a bunch of units with orders that just haven't moved yet standing around, there really needs to be a way to pick out the units without orders, like the aforementioned "next idle unit" button or an automatic cycling of all idle units like Civ4 does. I'm not bothered by having a dozen units I gave orders to last turn sitting around with full moves left, I trust that they'll move at the end of turn.. I'm bothered by that one unit I didn't give orders to, and the difficulty of telling which one that is, amongst all the other units that do have orders they just haven't executed yet.
That being said, it would be very cool to make movement order an option - let people check something to have Civ4-style moves at the beginning of turn, and everyone's happy. Or better yet! We should have a hotkey that forces all units with orders to execute them - so you can view your units, change any orders you want to, hit hotkey to prompt any units you gave orders to last turn to carry them out, then see if any still have movement left. [Edit: great minds, MT Silver beat me to it.]
Incidentally I don't have any problems with cities, the empire tree works very well for them, a "next idle city" button wouldn't hurt but I wouldn't use it thanks to the tree. It's a handy shortcut for champions too, but it doesn't cover normal units and would likely become too cluttered if it did - for those units we really need a next idle unit button or automatic Civ4-like cycling.
Also, the game seems to consider champions in cities 'not idle' by default - this is a problem, it's very easy to miss a newly matured son/daughter. They all should be flagged as idle when first created, until you specifically tell them to fortify or give them some other order - not the ones that have been moved into a city, just newly created units that start in cities. I assume it treats newly trained regular units the same way, but since there's no way to locate idle regular units anyway, this is a moot point (at least until we get an idle unit button).