I think the upcoming trial of Saddam Hussein will probably lead to new tensions between the U.S. and Europe, with some potentially harmful spillover for the Democratic would-be-nominees.

It seems likely that if Saddam is tried by an Iraqi court, that court will have the authority to sentence him to death - an option unlikely to be discouraged by the US. And it also seems likely that even most death-penalty skeptics in the US - a smaller group to begin with than in most other countries - would, with respect to Saddam, adopt the position of Hank Hill from the TV show King of the Hill: "My position on capital punishment? As close as possible to the switch."
(This is to say nothing about the powerful practical reasons for Saddam to be put to death: Much was said about how the spectre of his possible return hovered over the Iraqi people and inhibited their cooperation with the Americans and their willingness to develop a free society; it's possible the same fears could return if Saddam is sitting in an Iraqi prison with many of his former loyalists still on the loose.)

By contrast, the consensus of the international war-crimes trial establishment (an awkward phrasing, but it aptly sums up the combination of NGOs, academics and journalists who have done great work on the subject, and European and other governments who are most active in advocating such trials) is, it's safe to say, that capital punishment should never be an option (and that only those barbaric Americans could feel otherwise). Things have changed since the Nuremberg trials, notwithstanding Saddam's efforts to live up to the example of those who were executed in 1947.

The difference between US and European attitudes (at least among their political elites) towards capital punishment has long been a source of transcontinental tension. I think that a potential death sentence for Saddam might present another opportunity for the usual suspects to preen about how they cannot possibly be involved with such a corrupted process, and that the aid that may be promised to Jim Baker will therefore be delayed or reduced. (Scroll down to the last two paragraphs in this item to see how these concerns might even affect England.)

Will the nations who had no problems aiding a country that featured the death penalty for untold thousands of innocent people, develop scruples about aiding that country for using the death penalty for the murderer of those innocents?

Put that way, the question almost answers itself. I hope I'm wrong.

Left to their own volition, the potential Democratic nominees should not be affected by any flare-up on this point; most Democrats who dream of higher office have made their peace with the death penalty when politically necessary (with respect to Kucinich, insert the classic P.J. O' Rourke abortion joke here).
Wesley Clark might not be so lucky. He has advocated the imprisonment of Osama bin Laden instead of execution. While that statement is unlikely to haunt him too much unless (hopefully soon!) bin Laden is in fact captured, a big part of Clark's platform has been to accomodate the concerns of our European allies. Will he be tarred with their anti-death penalty absolutism and be placed in the situation of defending Saddam? Not likely, but it might make for some uncomfortable moments.
(If Clark has made a statement with respect to Saddam similar to the bin Laden one linked above, or if he does so in the future, I expect it to be featured in GOP commercials if he makes it that far.)