Does mixing Dominion expansions lessen the power of card combinations in random kingdom setups?
Added: A fundamental property of Dominion is card interaction, so to claim (not that anyone has) that a certain expansion doesn't increase the amount of positive interaction between cards/sets would be quite a criticism of said expansion. It's possible, but I haven't seen it yet. (Of course, Alchemy does create a sort of artificial exterior game with the potions, and some dislike it for this reason. But I digress). 

So what I should have said from the start is that every set is designed to make games more interesting, especially when combined with other sets. Also, the main way that I have developed strategy over the years is to look at a (random) set of 10 kingdom cards, and start looking at the interactions. As you'll see below, you can use (the cards that you add to your hand with) Scout for two major purposes: trashing, and discarding. So when Scout is in play, I quickly (?) decide if either of these is a viable option given the other cards out there, and then do the same for all the other cards and their main uses. 

Consider the combo:
Golem (Tactician, then Library/Minion/etc)

There are other examples, but they aren't fresh in my mind (I quit playing after 2000 something games on isotropic, and 1000 on BSW...).



Added:
While I stand by my answer, it seems that the best answer to this question would involve, at the very minimum, an analysis of how every card interacts with [all the other] cards from other expansions. At worst, we'd have to consider all 10^14 possible sets of kingdom cards! 

Here is my analysis of Scout:

Scout: Like the Apothecary, Scout can be used to add 3-4 cards to your hand (which may not have that great of a direct value - e.g. coppers/estates). Then you can combo (for different reasons, effects on your deck) this with:


Ambassador. 
Warehouse
Vault (+ Tunnel = BOOM)
Apprentice
Transmute
Forge
Hamlet 
Horse Traders
Young Witch
Hunting Party
Crossroads (!! Forgot about this one...)


Furthermore, with Hoard, the strategy of using Scout to get cards in your hand for the purpose of trashing opens up more possibilities. Scout is a good counter to Rabble. Scout might be the only +Action in the set, so then your only option to net an action would be to combine this with Golem, KC, or Throne Room. This is, of course, the last thing that crosses my mind when analyzing a set of 10 cards in-game. 



And then there's Scheme, which in itself opens up combos with most Action cards!

Analysis of Black Market:

Besides gaining a card that no other player can have, Black Market opens up a unique set of possibilities due to its extra buy phase. So during the execution of Black Market, you can [put into] play all of the treasures in your hand, possibly leaving you with 1-2 Action cards. In any case, you still have the +$ to spend from those treasures! If the other cards are, say, Library or Minion, then you can draw a bunch more cards and have a longer turn. If you are left with a Tactician, then you can use that to start your next turn with 10 cards, and you still get to spend the money that was played during the Black Market!