I think there's lots going on here (from what you've posted, obviously you can't tell really unless you know the child really well), but things I would be thinking about;
i) She may well be an early developer - this doesn't mean she isn't bright or able, or any of those things, but it may mean that she does have times when she plateaus, and the gap seems to close with the other children - and if they are later developers then this can be exaggerated, children definitely learn in developmental spurts!
ii) It sounds like she is very good at manipulating numbers, without necessarily having grasped the concept of what she is doing - I got through A Level maths, got an A, with exactly this approach - I had very little understanding of what I was doing, but knew what the mechanical approach to each sort of question should be, and could then manipulate the numbers correctly. This might explain why word problems seem harder - if she hasn't yet clicked what she is actually doing when she multiplies two numbers together etc. You can practise word problems all the time when you're out, just with simple calculations about things you see - eg, instead of saying things like 'what's 20-3?' try saying 'oh, look, there's three cars waiting at that traffic light, I wonder how many more we'd need to make 20....', or that sort of thing (that's a very basic example, sounds like she'd need more complex ideas).
I do think maths is divided up into the 'conceptual' and the 'numerical', and you need a grasp of both really!
iii) WRT silly mistakes, get her to do a 'sanity check' - try doing the question the other way round - so, using the above example, if she's done 20-3, and said 16, then say, ok, so what's 16+3? And she can check it that way, because you're less likely to get them wrong both ways round!!!
I really wouldn't worry, a level 3 is fantastic at age 6 which is what she'll be when they do the SATs, and certainly when my older kids did them, they didn't differentiate levels within the level 3, though this may have changed.