OK highlandman i'll give it a go..
1. population explosion is not actually an issue. Going forward the trend is for a slowdown of population increase as more countries come out of poverty and the numbers of kids per family is reducing. So potentially a non-issue in about 30 yrs or so when the world population is set to stabalise.
2. Security of food production and supply is an issue right at the heart of space exploration. What are they going to eat on long interstellar space journey's? We need to develop the technology to grown food in environments that are not ideal. So lots of genetically engineered stuff and technologies that can replicate the conditions on earth that plants and things need to grow.
3. Climate change needs a whole host of technologies to enable us to increase our energy requirements whilst reducing the impact on the planet and not relying on resources that are limited. Again - an issue that goes right to the heart of intersellar travel.
4. Misuse of natural resources - we're in the process of tidying up our acts and recycling more stuff stuff and being far more efficient with the planets resources. There is a long way to go yet and this needs to be taken to a whole other level to enable interstellar travel. Remember the end of Back to the Future and the fusion device that generates the 1.21 Gigawatts of energy from a few Banaskins and some rubbish from the dustbin - well that's feasible technology that someone somewhere is working on (the fusion reactor, not the time machine). Imagine what current problems that would solve in today's world.
So these things are completely implicit. The Planet Earth is just a very large space station and all the problems we face on the Earth are exactly the same as we will face in space. We just started out with a ready made space station, wheras for interstellar travel we will need to invent, engineer and build one. So clean and sustainable energy, secure food supplies, managing atmospheres and climate, doing more with less resources, reusing and recycling resources - they're all problems that need to be solved if the Human Race is to continue and thrive, both on Earth and in space.