I think that one of the most striking constitutional implications about the Louisiana Purchase resided with Jefferson, himself.  Jefferson was a strict Constructionist.  This meant that he believed that the understanding of the Constitution should only precede from what it says.  The "spirit" of the Constitution is in its specific words and language.  For Jefferson, more problems arise when individuals seek to assert what the Constitution "might say" as opposed to what it actually does so.  In the purchase of the territory, the Constitution did not specify how to acquire such a land through money.  The Constitution does not specify how the President is to proceed.  If anything, Jefferson understood that the Constitution suggested that Congressional approval of treaties is essential to the functioning of the system of checks and balances.  Jefferson could negotiate the treaty of the purchase, but it should be Congress' role to approve it.  Jefferson understood the difficulties in his purchase, his role as an Executive, and operating in a difficult terrain that the Constitution might not have addressed.  When Jefferson writes in his diary that "the less we say about constitutional difficulties the better," it indicates that Jefferson, himself, understood clearly the Constitutional challenges in purchasing the territory.  I think that this becomes one of the strongest implications of the purchase, in that Jefferson understood himself where the constitutional challenges existed in the purchase.