It bothers me that so often science and politics or science and religion, or even all three get mixed up.  This is, in fact, a major weakness of modern elected-official republics.  People try to get their way about issues through politics rather than what works best, expressing biases and ideologies and prejudices through the elective process.  Government is not the place to enforce morals and should be interested not in ideology but in what makes for the best outcomes for the population as a whole.

An example is the environment, and especially the global warming issue.  The environmental extremist ("tree hugger") would shut down modern commerce and industry to preserve some air headed idea of nature, when in fact nature left alone is no utopia.  On the other side of the political fence the political right engages in denial that the environment must be protected and in particular that mankind is causing a steady global warming, of which there is really no scientific doubt, that at best is going to cost billions and displace as many and at worse could lead to runaway warming converting our planet into another Venus (not that that seems likely but it is a possibility so severe that even though the chances are remote it must not be ignored).

Another issue of this sort is abortion.  Many religions, including my own, feel that any taking of life, including that of a fetus, is wrong -- and late in term seriously wrong.  However, the use of the political apparatus to interfere with such personal decisions leads to even worse wrongs.  It is fine to encourage having the baby and to set the right personal example in these things, it is not fine to use the criminal process on what is essentially a political issue.  I find the inability or unwillingness some express to see the point here that it is necessary to criminalize murder but not necessary to criminalize abortion makes all the difference unfortunate.

One final example of how modern political republics so often fail because of their structure -- the constant political interference in the curriculum of secondary and even tertiary education.  Science (especially evolutionary theory but also accurate and not grandiose histories or things like religious myths taught as history) leads to a misinformed and prejudiced public and is in the end harmful to such a culture.

This is one general area, then, among many, where single party states and even autocracies are better.