The platypus is proof that God has sense of humor. 
Or, perhaps it proves God is just plain mean.
1. mathematics and logic (science can't prove them because science presupposes them),
Science does not presuppose mathematics, as it was discovered by primitive humans using simple observation. Since then, mathematics has been used as a tool for science. As for logic, it is mind-bending to think about proving it, but here is something you can try. Simple logic tells us that slicing off our hand with a knife would result in the loss of a hand (duh, right!?). We know this, even if we have not experienced the slicing of our hand - as many here would put it, we have
faith in logic. But the difference here is that we can test our faith. Take the knife and actually slice off your hand and see what happens. You'll find that your logic is correct!
2. metaphysical truths (such as, there are minds that exist other than my own),
What about CAT scans, that clearly show certain areas of the brain are stimulated whenever you think about certain things? When asked to remember childhood memories, for example, certain parts of the brain show more activity than usual. Isn't this evidence of a "mind"?
3. ethical judgements (you can't prove by science that the Nazis were evil, because morality is not subject to the scientific method)
Assuming that all morals are relative, then yes, you cannot prove good or evil. But if you treat "morality" as a scientific concept and lay down rules along the lines of Isaac Asimov's Three Rules, then ethical judgements can become scientific. Besides, there is an ethical way of thinking that invloves using logic to determine what would be best for yourself - that ethics reasoning for you. Now this is of course all very arbitrary, but still it is science.
4. aesthetic judgements (the beautiful, like the good, cannot be scientifically proven), and, ironically
Actually there have been many studies on beauty that show a general trend among humans. For example, a survery was given across many nations and cultures (including primitive tribal ones) and in the survey, participants were asked to rank 25 faces in order from most to least attractive. Results differed little, regardless of where the survey was given. This suggests that within all humans, there is a very powerful way of "determining" if something is beautiful or not. Scientists could then use the survey data to come up with criteria for a "beautiful" face - criteria that surely not everyone agrees with, but critera that almost everybody would agree with. Among the criteria were listed symmetry, facial features porportional to the golden ratio, and skin smoothness. Similar studies could easily be done using other things besides a human face, and results would be similar. Of course, scientists don't know exactly why humans find symmetry and golden ratios attractive, but I suspect that they will eventually.
5. science itself (the belief that the scientific method discovers truth can't be proven by the scientific method itself)
Never really thought of this myself, but let's do it just to be pedantic.
1. Observation and description of a phenomenon or group of phenomena.
I have observed that the scientific method frequently delivers consistent information, and the information generated by the scientific method is of practical application in the world around us.
2. Formulation of an hypothesis to explain the phenomena.
It follows, then that the scientific method itself works in such a way, as to deliver correct and useful information.
3. Use of the hypothesis to predict the existence of other phenomena.
If the scientific method works in a way that delivers truth, that means that results given by the scientific method must themselves also work in a way that delivers truth.
4. Performance of experimental tests of the predictions by several independent experimenters and properly performed experiments.
I can't do this by myself, but I can contribute.
Observation: In olden times, a trip to the butcher with an animal carcass meant that inevitably one would have to battle flies the whole way. Obviously, the rotting meat that had been hanging in the sun all day was the source of the flies. Where do the flies at the butcher shop really come from? Does rotting meat turn into or produce the flies?
Hypothesis: Rotten meat does not turn into flies. Only flies can make more flies.
Prediction: If meat cannot turn into flies, rotting meat in a sealed (fly-proof) container should not produce flies or maggots.
Testing: Wide-mouth jars each containing a piece of meat are subjected to several variations of “openness” while all other variables were kept the same. Presence or absence of flies and maggots seen in each jar was recorded. In the control group of jars, flies were seen entering the jars. Later, maggots, then more flies were seen on the meat. In the gauze-covered jars, no flies were seen in the jars, but were observed around and on the gauze, and later a few maggots were seen on the meat. In the sealed jars, no maggots or flies were ever seen on the meat.
Conclusion(s): Only flies can make more flies. In the uncovered jars, flies entered and laid eggs on the meat. Maggots hatched from these eggs and grew into more adult flies. Adult flies laid eggs on the gauze on the gauze-covered jars. These eggs or the maggots from them dropped through the gauze onto the meat. In the sealed jars, no flies, maggots, nor eggs could enter, thus none were seen in those jars. Maggots arose only where flies were able to lay eggs.
This test of the scientific method clearly shows that the results it delivers are truthful and accurate. Would anyone else like to test the method?
-----
But my real question is why did you bring this up? Are these supposed gaps in scientific knowledge enough to turn one away from evolution and towards creationism? Sadly, the common tactic of a creationist is to attack evolution when any fault or inconsistancy is seen, while giving little or no proof of thier own stance. (If you didn't mean to do this, just ignore this!)
Topic: evolution vs. biblical theory