I've got a ten gear cassette in the rear and the top gear is fine. But, if I'm in my next four or five gears before the top gear I get a clicking noise of the type you get when you shift and it doesn't quite make it to the next gear. The noise is worse if I'm in my lower gear up front. Also, shifting down in the rear is a little wonky. It is a Fuji Cross Comp.
If the chain is running smoothly in the top gear (the smallest sprocket) but it runs poorly in the larger sprockets then it is most likely that the cable tension is too loose. The cable tension pulls the chain onto the larger sprockets. Insufficient tension means it won't change cleanly on to them (which I think is what is meant by changing 'down' a gear) and even when the gear has changed the derailleur won't be aligned properly and the chain will be noisy.
The reason the smallest sprocket works OK is because the position of the derailleur is limited by one of the adjustment screws at that extreme.
The most likely cause has been given by Daniel R Hicks' comment above "in the first few hundred miles, the cables stretch a bit".
You can tighten the cable by turning the cable adjuster anticlockwise. Use small changes as these 10-speed systems are very sensitive.
If you can't find the sweet spot with the adjuster then it is also possible that the derailleur has got knocked and is no longer aligned properly.
You are just cross chaining. Bicycle drive trains are designed so that if you are in your small chainring, you should be in one of the larger sprockets, and vice-versa. The chain is meant to be relatively parallel to the center line of your frame. When you deviate too much from this, the chain will rub on the derailleur. Cross-chaining is advised against because it increases wear, and you likely have a similar ratio with a different combination. It's not so bad to do it once in a while though.
Your front shifter may have a trim setting, which is kind-of a half-click between the main gears. This is a setting so that you can move the derailleur a little so that the chain won't rub when you are cross-chaining.