Therr are a few problems with this pardon, hence the stink.
Generally pardons are given at the end of a Presidents tenure, so this an anomaly, but who cares - that's irrelevant.
What is relevant, and why there's a stink, is that this particular pardon is a big FU to the Constitution.
Trumps pardon of Arpaio is problematic in the sense that it drop-kicks the separation of powers inherent in our governmental system.
Sure, sure, a sitting President can pardon anyone he or she wants, and there doesn't seem to be a proscribed limit to that power.
But, forget Trump and Arpaio for a second.
This sets a precedent in which someone who violated the law, violated the Constitution, was then found guilty, gets a free pass for simple political reasons.
Again, forget Trump: if this flies, any future President could say, 'Hey, I know it's unconstitutional and illegal, but do it anyway, I'll pardon you'.
The powers of government are separated for a reason, but Trump's pardon of Arpaio is an end-run around that separation.
If something occurs, and a citizens only redress is through the courts, but the Prez says, 'Wrong!', and pardons anyone who does his bidding or is politically aligned or is a friend, then we're hitting a Banana Republic style of government.
You may personally like Arpaio, and have no problems with his pardon, but there's always a next time, with a different President.